3/4 Mathematical Structures arising from Genetics and Molecular Biology
Formal Metadata
Title 
3/4 Mathematical Structures arising from Genetics and Molecular Biology

Title of Series  
Number of Parts 
18

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 

Release Date 
2013

Language 
English

Content Metadata
Subject Area 
00:00
Group action
Multiplication sign
1 (number)
Water vapor
Grothendieck topology
Explosion
Mathematics
Roundness (object)
Manysorted logic
Different (Kate Ryan album)
Orthogonality
Position operator
Amenable group
Physical system
Coordinate system
Price index
Lattice (order)
Variable (mathematics)
Thermodynamic equilibrium
Category of being
Order (biology)
Normal (geometry)
Right angle
Spacetime
Algebraic function
Point (geometry)
Functional (mathematics)
Divisor
Transformation (genetics)
Connectivity (graph theory)
Letterpress printing
Graph coloring
Product (business)
Force
Frequency
Modulform
Selectivity (electronic)
Condition number
Dependent and independent variables
Distribution (mathematics)
Matching (graph theory)
Projective plane
Expression
Independence (probability theory)
Basis <Mathematik>
Incidence algebra
Sphere
Voting
Logic
Large eddy simulation
Thermal radiation
Combinatory logic
Object (grammar)
Maß <Mathematik>
10:51
Dynamical system
Group action
State of matter
Multiplication sign
Range (statistics)
Nonstandard analysis
Insertion loss
Mereology
Food energy
Order of magnitude
Mathematics
Coefficient of determination
Manysorted logic
Different (Kate Ryan album)
Atomic number
Körper <Algebra>
Position operator
Physical system
Process (computing)
Generating set of a group
Moment (mathematics)
Maxima and minima
Lattice (order)
Surface of revolution
Complete metric space
Sequence
Measurement
Category of being
Quantum mechanics
Order (biology)
Quantum
Normal (geometry)
Right angle
Summierbarkeit
Mathematician
Resultant
Directed graph
Spacetime
Point (geometry)
Functional (mathematics)
Transformation (genetics)
Drop (liquid)
Graph coloring
Theory
Power (physics)
Product (business)
Number
Element (mathematics)
Frequency
Goodness of fit
Operator (mathematics)
Energy level
Condition number
Addition
Standard deviation
Distribution (mathematics)
Dependent and independent variables
Scaling (geometry)
Prisoner's dilemma
Weight
Model theory
Algebraic structure
Total S.A.
Basis <Mathematik>
Evolute
Convolution
Game theory
Object (grammar)
Pressure
Marginal distribution
Local ring
Maß <Mathematik>
30:05
Group action
State of matter
Standard Model
Euler angles
Multiplication sign
Equaliser (mathematics)
Set (mathematics)
Perspective (visual)
Food energy
Sign (mathematics)
Estimator
Different (Kate Ryan album)
Matrix (mathematics)
Diagram
Position operator
Stability theory
Physical system
Law of large numbers
Staff (military)
Measurement
Flow separation
Category of being
Isomorphieklasse
Normal (geometry)
Right angle
Figurate number
Spacetime
Point (geometry)
Student's ttest
Inequality (mathematics)
Product (business)
Power (physics)
Number
Element (mathematics)
Frequency
Causality
Wellformed formula
Modulform
Standard deviation
Multiplication
Forcing (mathematics)
Projective plane
Model theory
Physical law
Content (media)
Paradox
Algebraic structure
Basis <Mathematik>
Division (mathematics)
Approximation
Spring (hydrology)
Network topology
49:20
Randomization
Group action
Presentation of a group
State of matter
Euler angles
Equaliser (mathematics)
Multiplication sign
Sheaf (mathematics)
Set (mathematics)
Water vapor
Insertion loss
Parameter (computer programming)
Food energy
Grothendieck topology
Subset
Explosion
Different (Kate Ryan album)
Analogy
Flag
Position operator
Physical system
Area
Process (computing)
Sigmaalgebra
Moment (mathematics)
Measurement
Category of being
Arithmetic mean
Exterior algebra
Normal (geometry)
Right angle
Mathematician
Fundamental theorem of algebra
Spacetime
Point (geometry)
Classical physics
Suspension (chemistry)
Functional (mathematics)
Existence
Momentum
Number
Power (physics)
Prime ideal
Frequency
Goodness of fit
Operator (mathematics)
Energy level
Modulform
Analytic continuation
Condition number
Addition
Distribution (mathematics)
Standard deviation
Forcing (mathematics)
Projective plane
Mathematical analysis
Morley's categoricity theorem
Mortality rate
Line (geometry)
Limit (category theory)
Spring (hydrology)
Logic
Musical ensemble
Object (grammar)
Pressure
Limit of a function
Maß <Mathematik>
1:08:40
Group action
Direction (geometry)
Equaliser (mathematics)
1 (number)
Set (mathematics)
Insertion loss
Student's ttest
Inequality (mathematics)
Dimensional analysis
Theory
Subset
Number
Explosion
Morphismus
Mathematics
Different (Kate Ryan album)
Position operator
Physical system
Social class
Standard deviation
Dependent and independent variables
Weight
Prisoner's dilemma
Model theory
Projective plane
Mathematical analysis
Content (media)
Basis <Mathematik>
Sequence
Approximation
Category of being
Elementary arithmetic
Order (biology)
Right angle
Family
Arithmetic progression
Spacetime
Directed graph
1:18:36
Group action
State of matter
Standard Model
Multiplication sign
Equaliser (mathematics)
1 (number)
Set (mathematics)
Water vapor
Open set
Mereology
Food energy
Perspective (visual)
Vibration
Mathematics
Different (Kate Ryan album)
Length
Social class
Physical system
Area
Compact space
Process (computing)
Regulator gene
Gamma function
Gradient
Moment (mathematics)
Stress (mechanics)
Maxima and minima
Measurement
Category of being
Proof theory
Wave
Arithmetic mean
Shooting method
Isomorphieklasse
Klassengruppe
Order (biology)
Normal (geometry)
Right angle
Sinc function
Spacetime
Point (geometry)
Functional (mathematics)
Variety (linguistics)
Real number
Number
Product (business)
Element (mathematics)
Frequency
Goodness of fit
Reduction of order
Modulform
Lie group
Condition number
Scaling (geometry)
Matching (graph theory)
Projective plane
Basis <Mathematik>
Incidence algebra
Mortality rate
Limit (category theory)
Formal power series
Combinatory logic
Glattheit <Mathematik>
Game theory
Object (grammar)
1:37:48
Group action
INTEGRAL
Latin square
State of matter
Multiplication sign
Decimal
1 (number)
Water vapor
Mereology
Food energy
Explosion
Mathematics
Different (Kate Ryan album)
Physical system
Process (computing)
Moment (mathematics)
Physicalism
Measurement
Discounts and allowances
Category of being
Arithmetic mean
Quantum mechanics
Quantum
Right angle
Conformal map
Spacetime
Point (geometry)
Existence
Statistics
Functional (mathematics)
Real number
Number
Causality
Wellformed formula
Complex number
Reduction of order
Modulform
Energy level
Condition number
Distribution (mathematics)
Projective plane
Neighbourhood (graph theory)
Physical law
Commutator
Algebraic structure
Field extension
Universe (mathematics)
Object (grammar)
Family
Funktionenalgebra
Maß <Mathematik>
1:49:34
Classical physics
Point (geometry)
Presentation of a group
Group action
Multiplication
Functional (mathematics)
Equaliser (mathematics)
Connectivity (graph theory)
Projective plane
Survival analysis
Product (business)
Number
Power (physics)
Mathematics
Different (Kate Ryan album)
Term (mathematics)
Operator (mathematics)
Condition number
Directed graph
00:07
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01:17
BlackBerry on a and what have is a function that function of the store and that so you don't concern is with function to all concerned component of these may be more damaging she sure that you think about this kind of violence he like that and you have distribution than the population to have this kind of some wait the only thing the that probably able operate on the label when you think about what had happened Sunday and amenities and remains population toward the change right there don't change the whole genes with only and not allegiance portal as was done in by both amendment implicitly or explicitly backed out of special case you're out the closet indicating the medical system so they can kind of get a baby came from Estonia summarized what these system so there is some logic allows an indicator of indicators of genetics is being planned print on the incident but In many variables you lied by putting on dignity In each year less than something they want in the it could also deal June they certainly not you and I can stand here and put them in the quite way the Lake well will shape of in particular I would say was property of this out of which implicit in Computational Genetics in it and if you don't make it the police said complicated has spread from person because of Spanish potential 2 of algebra its selfish official more subjective so that promote studying this for free trade in the eye and the English daily log but if you look at this property of the Spanish and the fact that it is not all is quite but a marketable features are the editor and would appear the report said which is implicit in the Internet and so much in the way of the transformation of information call in 2 stages of that and more the problem is that so high and water's come come come to life in an example of them here because some of the certificate algebra functions somewhere depths and space and in the more colorful maps Spain in the case of Mandela in the year you used space in the quarter and you'd have projections according In this projections yeah and I'm 1 of the fastest time the in the morning but we have no interest in that region important some consequences so he heeded the whole story started with both his allies demanded logic into a big men will tell you when installed in this 2nd round of the production of production to him population makes now have you had appropriations different than that but we need need to get to do that change so that the slogan of the fugitive so I've doesn't apply just happens to us and guys new injuries and the site was still going to be people found out so much and had some pretty destroyed everything that justifiable because it was the worst kind and that it's in their interest Simmons behind the 1st layer of projections for the quarter was probably going equal set on the 2nd day of my life and then we have a new kind of match them up to peak at the end of March that doubts about but of its not because in there isn't going to material "quotation mark amusing he said that the old chapter and typical met with Thai pursuant the meeting the light goes quite remarkable "quotation mark among and the more than a year after the 1st year round as the match it is a matter objective Facebook and the sphere of the Ministry of and at any of it after they had been here for 1 of the space taking careful medical school and become company a so you may express opinion on Monday is wasted space was prescribed form in the initial projections based request submitted sphere factors projectors based the projected wastage in the example you have still bring the to the fall by way the quite remarkably semantics its sitting there on the death orthogonal and now the inside of the sort that we have this is the point of unity and that's because rescue independence of its independence assumptions and those from from that article point of view it as an independent with like it means you have to think that America is can and the wild immediately and then the next leg of this has assumed g single and the head of the matches should get this way motivated from the water and have the property of most of the work of the match which mental emphasized school was I look at it but that it appeared features such as the the distribution of population changes on the 1st round of random randomly start knocking selection so if you have a population radiation with about 100 object is not to say that just last month of present them and then the next day when and if something big and explanation in the morning and this more intimate and it was the best combination positive otherwise nothing right and you don't get you don't get anything anything manageable communications respondent has several genes and this kind of communication now doesn't symbolizes that that renders the blind but exponentially convergence and the reason that began the kind of man you see in this example to here you are the fundamental in the modern projections the newspaper out of them you may think and then you find that there would be a major group and it's exactly what the coordination group because of the security you can control them pretty well and the rest basis of the 2 men will have to work with conditions such case the simple conditions he has the right to the point in the match between the equilibrium position and it is fixed .period apostrophes financial the this because that's what astronauts local attractive and according to the normalization of different factors then you know it's attractive interactions throughout tool equilibrium position everything going up space of equilibrium in the medium and large mature at the end of this month and and and In get the capital last nite biology should should be said that that this feature has put the fundamental property of sexual producing quantities that it's not features which I that but the secret units of gunmen inside the visible it should be the popular if not for that we'll be 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10:51
might not be good documentation that you can use the data and there will be BBQ range in population and that is not designed to generate change when that is not sexually production standards of course and independent depends this but but essential huge makes something that is incompatible more stable the population keeps Union which manifested itself in intensity they become so acute that some other the companies in addition to a completely different game at home to look after with start and injured to timescales was the 1 she described from many of the world's scale the last respond to mediation because his age and be may have subject some modifications which and dog do them there's just something and and I mean that in in the traditional version of the American confused confused by people but some people have had at that time and that become but the recent there were some traders had been achieved but it may be deceptive because it was happening many times when that country theory everybody was those who supported him during a prison or not understand evolution and then they generation carries Mendel and then with the money by Albanian and fish and the right to develop mathematical formalism on and on the computer is not only understand and this was called Modern pollution and this is about 3 times that and then molecular Bolger status among all the grave of great above this time said that well now we understand evolution on the molecular level he was at the weekend sarcastic about everybody else in the people out both speaking about revolution and saying they understand that you've got the opinion justifiably then this nothing but none of them and understood as people because he's going to go around to the view that and say that we understand the need and the reason is because the the day doctor on Monday because of the pet basis of selected the use of units of the EU cook but for the fact that abided Friedman would be even could in the novels is the total amount of racist sequence not being analyzed think of the order and the than if this but this is that of rendition of 10 sound and the statement about the adoption with any of the subject than to the 5 who was that memorial again is incompatible some money now people say Well I understand something right again and consider the common ancestor of all according to received about 13 . 5 billion years ago the lack of a better life it explicitly stated that we understand that this is the time to be sure that the nation with international companies that people believe believed in 200 years ago so concerning that and I want to return to the end and this year and so the point I believe that the 1 last point that this was a special kind of and the unless etiquette immediately asked What are the formation of this kind available when Helen algebra this kind of dynamics and there are other examples where there another pronounced example you that was normal so come from the same day as the row 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energy source but the model wouldn't mathematics was think to pursue and so was amusing about the mathematics which you have physical or biological united to take money and the result is the same but the interpretation depends on bag so what is the logic of Of all the more so have to plan for that time I kind of the same conjectured that you and justifiable because it is out atoms in the classical frame that can exist just absurd notion that don't make sense in the quantum quantum mechanics and find something to eat and but you can only pretend them you want to understand this system consisting of many at the time and the interview was kind in the play about take that ideology of all 1 of the few you can bet and it is just a lot of things in the
20:42
so what we have a system and what states and so even if it is how it was done the mathematician interpretation is coming along you can think of said can theory of the winning margin disputed the idea you will be based unit elements of that 1st half the set of and this is lot of the Canadian of space right now we have a policy position of the and the immediate objections carefully the itself has not it's not good enough to be finished as the indirect but of course did this because yeah the 2 in the languages of the property that is what I want to explain to the way people I didn't want to listen to it was just a bit of a language from the kind of turning point the magnitude of 1968 particular purpose I would so pretty good I think people poisoned and of course the other people involved particularly the story was people accompanying defended in the way of thinking and then another point was that understand we developed but it was not stands as you because before so what Morrison said can be interpreted as complicated as the impact of nonstandard analysis and 2 article which together all of this without the consent of the facetoface with the grace of this abstraction mathematician but you may still have them the reason I think so what what action had this how what would that have been tampered with and where we expanded our transformative language the into bonds into claims and what you and you so his physical system for boys and was again at preferred to be critical I just yes for the purpose of the discussions that slightly so that you also think about the people that you know just happened to be in a letter genetic pattern in this space and this is the pressure of the Americans but know just a mental picture of what you do that merging the banks machine put it in waters and that its political system has its own state and you think about this something new and something thinking this In addition the condition that they can have such mission put it so well and have the same blinking and can lot the space and you have to get it together and this little morally and don't have a problem with you only have frequency of drinking and if you get 1 machine by Transportation Displays say they can't use them and then it comes at a point in green and from that you do concept and it's going to with the fetus is an yes it is what it is they can be used to great completed I described in categorical terms but appropriate there I think usually we took it because fact of how you do that in this protocols have morphed into getting and that the better but the kind of farming so that I might have tried simple more adequate familiar from Rome was revenue .period view of the was human peace so what is meant to be 1 of the few ecosystem right and I want to say that it is not that we should be effect and with the use of space the number of states with a specified number and not by the vendor stood in their way in an appropriate way executive person England words and sent it into the language of 1st look at what occur in 2nd into into danger dangerous that the fact that there is some growth in the group some them completion of the sale and finishing things this is just what so what you don't know a system is in a tight political think this kind of thing Reinking and sometimes you can it and sometimes you can have dream in the months ahead and there each of them the future systems are unique and attached to a small island shortages so you may as well all season this mission put him in this mission connected with permission to do that and so the would have get good the ministry described questionable category which kindergarten category but if he is said to everything becomes the the public and get basically of of all clients given the normalized total weight loss to match you with the measurement units and more than being a book about the same as said before that but maybe not a stone but drops of water the together so that we can bring together there must some an immediate objection will be just like fashion satellite good shows scenes that summarizes the thank you and the number to be concluded with but following 2 and a half and this is How can find pages can pointing to the Commission to find man and and frequent use of something here in the middle frequency how we would our measures based on on more reasons when you go from 1 that is what we should look the stage at the end of the legal system was probably better than anything at this time amendment and the making them away but the frequency and again when you look at the local media but numbers you on account of being in mortar from 1 final respects what about the beach right the people we want you may but by means of small and you know perfectly well what In other words it is "quotation mark I hung from the category of white space be good we have to think you know what I mean that I will let you know if you do want to see and then go on and just all measures that no call for operation from that all statements and further improved or registered up at this critical article was connected with the rightful just standards and is absolutely true that thinking in only 3rd and and what it was and is getting good resistance and this what people do in the but their language and their central English and this creates problems and historical so the point is interesting thing for me justification the distinguished bed was the enterprise In the inconsistent and become more active in the 1st place contained In this context something and you have no room for mistakes exactly because he was using his own which he could post a member of the modern medicine and at the same this is just the sort of problems through a you should know that if you make mistakes cost you have a pretty good idea and that the kindergarten the names of Sony erected you just just because complete ballast to cater and certainly mistaken about this because
30:06
that was connect best the cyanide and growth of and but this again concerned about concerned that the court issues with this he noted and so I think the point is to understand what is meant to build this kind of like and in the the poor again physical idea and to be something should measure many many times and the new station and get the people for the fall short of the prime space would be found to be dialog when I on the other hand if you and at the start end of this picture you you may have hidden identical thing can make and and take advantage of the measured began and look at the content of this measurements this was the message but however and and we've you want to count the number of states you have to go to repeat experiments to make them on the other hand is really going on in exactly the formula is not definitive and it's very efficient way to computed suggest and mistook the commission members just because you were going to make suggestions from the words black from but it's against a former not British Formula One Nation so what would be finished I end the Finnish gesture and a sign reading him I can't find my speech :colon plant if you have any to it economists assign and growth and a group of growth and the right so just showed saluted isn't right with have in the back of our minds between do the center and this means that we have this is the 1st assigned to market and sell something especially the group G formally by market forces Europe and the United States the comports energy than any of us in the position that the group was a professor of political I can In the 1st approximation and agreed is on a primary basis its emissions growth and a group a that but then at the stability the group with Citigroup isomorphic Ostpolitik elections this category also has an apology which I suppressed this 1 it was surprises with coming 2nd otherwise if you say that in the future I believe accountable for court but I do not fear the special spaces to look production by its topology or your do everything continues but in any case I wanted that bypass the industry become closer closer to the call of the extreme action what went out of her way to into In the initally differences among different perspective that's kind of the idea because in fact the correct statement it is not a new with this according but only nonstandard model the unit and find good important and we shall this comes to the more modern resulting in what he said when you have to use the standard model groups and and and and small getting but now I want to look at this and more in a way that would permit the following on surprised a lot and this week inequality and this is something that we had spoke about it they wanted to be together we have a duty to in again forced to think about other mathematical From a man In the spring of the actions of during his investment and you can the projection of 1 thing "quotation mark exwife playing American students projections at the projection by In the southern border of the steps of the exwife and surprised them 2 us recall that brought it to the shop but not for shoppers stands form I support amid quality because if you have man in the mountains of course but you should have some more and this is a warning to Waterman ,comma power estimation except that show him not not bad but it could be amusing because that's what you in the shop foreman to make powerful equality complied but I also believe in equality is happy with a microphone in the quarter and so how you prove that and this approved by we need to be in the interest of writing some simple computations inequality should not what kind of guy but the right way in my view that would think about it from growth and growth you that it has nothing to do with respect all was the product of Spain "quotation mark according to limitation excellent and have a structure and projected that's wages said and look at this matter halves and quarters and then you hear the structure of the European staff of everything about measurable system but it is obvious that attitude speech he admitted that it should have said is that abandoning ship the right I said magistrate found in the category of crime essentially it's going to be but this much about him being kind of some kind of figures procedures and it would be a lot these matters in the city of the world the stakes with the most of that just all everything this season because many president of getting what it wants the statement minister said that at the moment but on the other hand against that remember all some and and what you say that you could pick the at only go to the end that's what we can produce quality of life he was approximately something when it back and you may get what you want so what you have to rule on approximately half the and now again in the 2nd half of the comeback come back come back to in the 2nd if you don't quite too we wouldn't think a lot when you start going to kind of high power he will this
39:47
set of that will come of kind and so we have to secure with have according to way to the executives at Dubai and Cooper minus a something Germany and and then in the initiative quality and so completely before group and no 1 should think about that so what happens when the power and apply the lessons and I want to formulate lowlife numbers possibly see they wouldn't do that again definition growth in the group they don't need a system and then what is the point of all those numbers in this in this country so it applies to present patients find which want to write a collection it said the power of the street I think the thing and every 1 of them with a product that is remembered that the essence of this most demented mental type of Latvia it was exactly like that remember how you felt cannot quite apart from what How do I know many of the predictable said they were taking matrix we shall all normalized equals 1 I deeply byproduct of some he and son and normalized and activematrix understandably want to have a space made from space remains itself come from it was the kind of paradox by How do you make a special case those there now for many in the industry has decided to form a strong but that's about United from foot to wait to make the system work however is exactly what we are doing this square space out there in the point of saying that when it goes in the space can and some sense of despair is equal and fair would call homogeneous space will just equal and don't wouldn't want to say because the president but that is what I think about it being homogeneous of August almost afraid to audit his conceptual homogeneous leaders of it was so as to make space of time spent when highpowered become essential images and to say that the newly in compact with have to say that intake and meeting the standard in the larger number in this space has announced that the space is emerging up to higherorder and this led to pursue that you used to see if it did not let me remind you and what are the percentage definition in what sense and moral yet and this is what is essential is not only to for the Pacers who for more than it into an address for him and his arguing diagram of MEPs began the goal to tie the highpowered called that is approximated with .period diagram with old spaces are emerging and Morpheus which was used by the way when they spaces are homogeneous in more Morpheus homage to those adjust the composition of of right people of your projected the German great so we here have now but you and the number that you can use a U.S. offer to comports company and the numbers and it's getting constitutional just whatever numbers and get a good deal of of my mother because that word of numbers and containment and most people in this category convergence of not getting in with extreme not stand in the future ,comma muses In but then so in the United States exports because when have to decide the 2 of them together and speak effectively and fewer companies would want to have it expected the worst you don't have to witness the and is in no way just as if you just follow your good leaving tuition because he didn't want you do right as it was always about the justification that which is by is not time to justification because it depends how much commodities made in Mexico some people OK so what what is essential and urges them to colleges that don't have occurrences and they differ and at the end of the year eventually them up in monkeys .period editors structures premiere in numbers and commodity In the end of the year but have to to many places to find bridges and another magistrates is set close wipes and close 1 from another but he wouldn't quit doing tangible measures In many items from must if you don't take some mountain bike out of the way a lot of of steps and you do whatever you want to spread the condensed so this will be a major cause of action and then other 1 multiple here was used in normalization hopelessly connected and In other 1 you multiply you multiply everything by constant all multiple because of there if you want to hold open the gate divide along the cost of Basic Law of the number of elements in the space the get everything replied in the blunt instrument individual reducing trading inconvenient although that figure most its while an infant glass which means that there was a lot but you enjoy themselves so much as see the 2nd of 4 more than that of numbers and then become probably it except here is valuable .period because have spaces and the number of British 1 you do I have a small 1 but again can this convention because until you have a secret debate going on in the year of memorizing and amended by end August and then and these things that essential point again lost in the elections last nation small the shows forget not a lot in the past and destruction atmosphere multiplied by the number of multiply always been numbered dataset intercepted from the authorities acted interpreter had looked and all proved to cure you to have a separate group subject in writing and editing and subject enlightened and multiplicative and then they have to take it to spread his wife and power and she gave it to can bring lodged in their and called and boisterous debate is a glass of beer in the space but the In this case right 1st of all I and is so the number of items anomalies in the that defiance to take a lot number to be and there was year even on the eve enterprise ankle and computers and in end enterprise by weighing she's been you from just because the country competition because boys behave correctly and I have no idea the bicycle numbers and make you use look like numbers from 2 different buyers it is the law of large numbers fall already and the that's exact but you can't really have
49:21
From that point of view this is a better look a lot less than usual because it involves not exit random variable is just 1 of many suspect is the property of the categories and standard but of course my began in cheating because there are too many yeah secretly this race Speight and that space is equal to all and of course you and why some 4 boys and 2 space who was European Space with lying to men and it the 2nd measure distribution ensemble where they and became a social property of 2 United States space really have to wait long for this year's and this was how will think about the litigation and debris and I don't know exactly how much the way boys memorize questions as the but he arguing that the additional cost shows he these were in his head in mind of course most of the nite and was not I wasn't available for infected was well can establish a century ago by lightning and then came people you know quite a lot of questions would change at depths of about what was thought and the establishment of a boy who was just in the room on the fun of it and accusing the majority of Europe and with had pensions insisting standing on anyway this is this is a point that I just want to explain this so how using that you establish basic basic 1 fell 1 the basic was standing now come back to abstract MySpace and because the the report about 5 so what's happened spaces that France was certified as you find you found indicated on Friday and the fund is extremely simple just set of maps from acts that you find inspiration just at all madam we don't know what measurements of the quoted were scattered on the expertise of subcategory of that more of than this category is an appointment she the point is the point was enough to define usually manned space you have to speak about the whole set of measures in the center of the than continue therefore you do you will fall due to fact before and certainty that just nobody mathematician on this section could imagine pleasant 30 kilometers from the legislature and the institute should have cost them because it's important to its low shouldn't this means but as as it would only have to know that you this out for our purposes and in classical language and to really future potential defined in many areas in different ways but the point is convenient because you wouldn't you would I think that is meant to some and that he doesn't have to be France and in another way to think about what matched all measures spaces prime space escaping water pricing pressures it's going to be an incentive for the biggest loss of getting beset not just last and heal the top terrorist acts and is involved with just in the top speed and you bring in so what's what's rates of operations officer for petitions can intersect the emperor In operation called you have to pay on P and the meaning that physical system you human rights the state that Inc simultaneously focused how much consists appears possible in this case could and you don't get the call .period you don't know what in the news didn't kill settlements just to hear and it's not in a that the numbers of course rather than for obstruction and use them with me common is use to a new appropriations considers that everything should be somebody take acceptable but it seems that the experience of the last case well as the budget but it didn't work and just give better "quotation mark just I do so in this case fall under section in this again have you find it according to what it means to have fun the and function as a condition of getting going and then means following the loss to be gossip you and then the meaning of life are you get that and this get awarded his property but as essential waterfront assessed fines suspensions have probative I didn't that the Yemeni space means have found in this property yours and then all you have to know about me and everything concerning this language and extremely simple we have 9 but I think could well it would be the year of the Ox the School Committee according to copy of the notice that none of these operations of the operations from the point of operation of the ship and that's it again and this is something that might want to get there but said about it some the effects of what will happen with the saying forget about that to be differently and much much but to want higher levels which is so this would be the case I want a former Peru expressed the most basic equality and diversity according to the chairman equality says time to the end of at the end of last no it kind of of sites because we make 2 observations and the continuity of normal person if you make them together don't interact in there don't appear on the don't example the way certain Reinking and their computers in the independent of what number will multiply so long but in the interim some of them may prevent was into 1 if you and don't have fewer numbers and that he is aware that some because they already have a picture of me being from Boston now How can investment and think about it because people could prove with emotion do not understand this and that and quite the highcapacity consists of such where they don't know a lot of recommended friendship located in the world if you can't do get this fiscal year to get a good and then become obvious that without an impetus could prove that I was going to follow from the lead of such behalf when I was in course of a year put him in power but then would be in the car it becomes everything becomes and they will become major if you statement so that
59:01
we can moment may be identified only slightly different if you only have yourself and that's what it intends to do projections to P to kill it says here somewhere in the project here is my pick he McEwen the man he wanted to hear about position and this is and so said that about me he projection being his magic and people you the measure but not very powerful they all become homogeneous and would the icing on the steps in the broader people who requested here that is not on the fractured and this is somewhat stay because it is all more oxygen and how you use your and this is the kind of fundamental and serious complaints and that the public thinks this kind of understood this and this and that but bought for a few constituting condition categorical what jets and the point is that the exactly the appears in the bag I am going to be I was background is kind of object so when you go from there and get a good look at the category of such down and until someone who knows perhaps more and is more than a few days from what we communicated what it can do all the flags of the call then to be injected him with injected morphine and the sense of the word it is not good for me and the beach suggested for pop Art and father getting so that's that and monotone voice indicated waters "quotation mark if you have to from subjective more morph complete injected in the broadest sense that that the the fact according to another point not a quality and quantity more you use a slightly different and says that and of doubtful also included in the England assure you in this moment the advantages of the nation for more efficient and if you are finish so in that shouldn't this is called an alternative and city like that and all be home somewhat after more than 3 thousand presentation of course you never know who is behind it and secondly you think you will be called you and 1 of the fact that the time for me to be here exactly what about is so what happens Koppel and the like my friend the number of times mostly in in this context not by basically that go on minors hoping messenger item posted Mexico's however technical convened partially defined member but they're not dead the yield on the 10 site and take the categorical dangerous let it get you just need to allow passed by the defendants just for defining the apology but it was like but categories just go away In defining his property the story is the difference between those between the form of these how you're right when you arrive in July he listens to remember this from that owning and president but said he may computations insistence of also Pentagon makes sense was good about that was pretty typical for this logic you get to article dealing with entities of individual or being you sense in simple things and a pair of what indifference to interpret the data but recap of the boys being accused in the spring of being the defied the difference all of them walking on the front the more things I don't want but by someone who wanted him it would have more appeal than not of this is that the ongoing evaluation that category and that a more this executive powers that should not this kind of John bottles says that the the yesterday ordered more vertically a lot of of that it's because it would this call .period began expressed about everything .period going you don't need set the editor of the market should partial said functions that are all but out of it if he could have used to them at the time of the bacterium I would have preferred to have abandoned them alive political UK being undertaken John C. the the whole point of categorical language that emphasizes the recommendation and so is the Jets an official at the gate Albany job and this year you know know what to do with the argument that much more clearly linked in a deal I guess perfect and some drawbacks and just see them and we will not end that was 1 of the points you have to reconcile competing against audio and you have to spend the nite the world improper but my point was to show you this example become better use the people who have entered the method again from in every Member and different in different periods of time as the boys when using their people use therefore I think that the mean that Mozambique former of but if that of berating the job because have long formed force notably in 1 line Sunday was was that this it's about numbers since it was so this is not a problem With these kind died is useful climbing back to example so what should here in the UK and it would be just as was 1 which according to an analysis of the 43 and what was that ended any mail but is less recalled the plot of good analogy In according the cost from imaging this again to withstand logic of this limit into it happens emergency and you have to make the competition however this finally about 100 but you can prove the quantity calls only for Virginia that's what you do about approximation in but and for the units subject was from the heat and rigidity of not much but an to have similar cases and have a lot of Kansas Inc and why people with a wide the club but the existence of course have to jump from just separate you want and the addition of like mosques became an energy alike must be edited and reason with them with attitude the it's not explanation but some some phenomena that I think to the fishermen and and the but it's not that know that the police said heroin again with the bat that I had said in a short while now so I
1:08:42
we have this property and now I'm back the student was in fact much stronger inequalities still namely that a projection of you can the end here because you have to trust and think everything's discrete disputed thinking something I'd have described his former continue thing you can do it all again approximate everything minutes thinking this was subset of MySpace then blew subset ties and entered in the but projections indicated by which are smaller than Connecticut and the loss is still on course to to become stronger and when you come to analysis this response to "quotation mark socalled lost someone who wants to approve the inches saying the same thing strengthening of users of the recording of the country is much more my my money back get the dignity savings the problem with all the notion that he is not to allow federal for 4 or more being it is not a lot of different quality makes you think about it should be on the best you can do in the gas distributions of the but them to you and so it here I from the quantity in this number which descending on the city in the world is installed in the unity government of what might be the standard introduction of ordinary Germans across the south in order then you have to remember from all of the analogy such as some of the issues at hand is just all kind of defaults From there you go to 2 next step because we a system and what influences mean it system was critical of the United had the slightest had long had a particle and by the Committee for the minister 5 In each has brother so I have find space to the it was fun this information out of them likewise what kind of so what again so what you see this guy getting word according to the New Jack the 1 the idea is to build more morphism prisons provided dimensions based on the basis of the basic them up projection and they all have a lot the media From then on to the finance and approved the move ,comma so no 1 minded ,comma water problems for quite a while the issue Englishman but in this April formally speaking more generally but formerly in the hands so if you find space and ,comma was concerned the keys to indigent and they can cannot face fines you accuse of please come out and elections from sequences always peeled away you for example that maybe 2 items equal weight to to the theory of the the question is 1 the item between now that item somewhat between 2 spaces which can be used the action when you have spread inaction over here you get a good somewhat commuting the actions that have yet to get what construction and you want in this particular instance and not just come from that said I feel more if effective and someone is possible to comply and for course this was the 1st to you cannot sustain for any group such a picture the in company the is citizen was progress made by the next step and that but ,comma approved for use in the end the experience everything the same the report says that if it isn't doing but was not known because there never was worrying about onedimensional system again without interruption began to most fees being concerns of the system of particles and onedimensional recent but settings there citing in Nemesis system the bigpicture exceeding that of of a lot of attention by onehalf and the proving greater the city of much more complicated than that but even the basically we I had a bad thing about including a head script didn't understand these differentlanguage versions of this I'm curious is the source of of news but this was sure this was the 5th in front of condemnation it's a comfortable income generated by the same class but the French generic come on the policies company the Center for Language and it's not all kind of examples nobody can show me we knew we were in a step that would be not to buy any group that to show it was against some other questionable referred 30 exactly by this month than the model for the goes I will outline that analysis can spend and absolutely conclusion that's not my fault ,comma so the experience not at the end of looking good things that you have the group the stupidity of the symbol of the year the much more often actually prefer that changes to the economic picture we have to be simple defined what entered all of these kind of ecosystem and what you do directions so knows of former soldiers
1:16:41
experience working for the interests the it's in right since its invasion of course and to promote you have to mobilize 2 0 2 2 2 2 pieces huge self the head of the town of men become final by the end of his speech just emerging from what we observe on this because he wanted to take this and divided the of Arkansas by the Board Elections Gordon who may exist only in case of Nunavut except when it was introduced in this example is usually and in the evening looking so that was your headed by the chairman Orioles you tell them you know some of the content of the speech and a big piece more fees last year assessment so that things began inviting you too the problem we still have you can you make this an elementary school in back of make peace with the fact the young I have detected have detected and attack along but the musicianship who writes that is fine space and I can move along in a controlled the new position has been that the intake and make me many
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times take measurements and a normal life right so and so he she probably status but the point is of course will do the right thing by a cowardice charge movement but the speed limit and debris barely hit the ground but the point is akin to some of my many of the blind some you just for what I can and cannot and will probably affect them together and then mean and the 2 of the port in the enterprise is the these what he she is not what them there is no and feels always system appeared absurd idea because this kind of stuff would you be becoming the anyway but they were hardly likely to be revised up for it depends in the end of the scale is just not the states which have the with this data can observe the change change all the time that don't exchange of on the state when it goes from 1 to another energy being commuted after again by the end of the month American why from recession on departure I wouldn't you go away from this naive said so in fact could end to pick up the pace of the class of men and few but undermanned but their protocols used be to get it would link it to the 2nd the formalize maybe not in the media somewhat different kind show .period How many How many right and in the end and so I can have a good shot at the company's system over the detectives if you get a new 1 is set has to meet them in the game against him vote which means that if I get killed and managed to escape the peace and then they just made me my Canterbury afterward and was proposal the number would times the same as a year for a new apart all huge would have of course a son he did make my physical system much stronger energy to more and more wouldn't particularly acute so methodical it means that my kind of messed up said space as font that is determined by more morning on this but I don't think that's going to change my depends how could this exact thing and not step and that different from different founded on this understand system will you marry me and you you and you end up and then the point In particular In the end all the good of products based there and by information in the 1st grade B for a prompt project to you you pull system or from effect kind Joyce of all of the city of the other landed so when a man and dependency nothing to do these where food in general properties of water and you finish the product and customer service called and called and begged this is the future of men that's great for the moment have not I can imagine entered the decay of all of exactly so I just met and on and on they said and the and then some and appear to be at the low end of our people right at the peak of the hands and the government and if you do this is that someone like this and it would be equally and because of the added of that the group was Nunavut so don't you think we should you use hear that and last I lied and lost a lot for any of the things we just with a magical part of ,comma of everything jazz is kind of could you articulate and when and where with the such amazing that this community the rest of the home of an issue to be closer to the shore and this that the new you just want to try and sort that out the order space be following you buy get me onion the court In a decrease somewhat that debate In the and that's how the story was because by way it did before you make that demand that it is not too the opening of the new wave of stars such more reasons we shouldn't interfere and therefore it would be the same in all cities and then about capital you go to the polls before he hopes some larger class groups which had been found out that they not and piece of land but it to of and I somewhat but for the of offense the use of the American of the and the poorest African of Granger it's not directly in his latest brickandmortar provision his 1st was the message the idea that competition in the Committee of competition but so what is the point is that the classes where do I someone who up doesn't lie at the core and so the company that I wouldn't say if you has about groups some of the groups in the group of groups of linear an image of what called you find groups that means that is defined as suitable that is and and From the perspective of the game which may come back not usually found in in the future he should have far and and logical that the way you have to think about that this 1 excellent compact space it approximately confided that the abolition could probably be found can approximate action and said that effort in Regulation EC you find it so defying the will of the ones whose actions had set for 48 got disclosed the nature and that he had asked the court but the he is in his 2nd year in a variety of creating simple terms but in the case where we would that there are some of the groups all over nonstandard Compaq I have been in use since send compact spaces and then compacts with the compact space in the category of of nononsense met basis which
1:28:13
means all objects in when you take the standard model of the language of art of real numbers so when you have real numbers could have been in years and dramatic you understood the number but space that a behind that this group approximately on Friday but the ad in different rates for all From the wife the initiation 2 and so it was decided that a problem that distinctive conditions all and enable all the different groups Suffolk projected features of this but those who have received Nunavut Suffolk but they're more examples but we don't know the history is we don't like that and the information is quite Coke quite simple so if you decide not to send a nonstandard language which usually referring group already sunk in waters as means that if you have a convenient to have 1 infant a large number the number of measure of huge huge number 5 but largely on the story this is is about the to find that anything information is not that the industry is a mathematical formalism and we obviously you notified the but you an example the cheese a typical example numbers you can still find consider although there at the time the maximal type of income shooting machine is a problem in 2000 without all this you would have more wanted where computer is viewed as a moderate and right problem we go for it myself because only those who stopped see how long it takes and indeed the suppression of all the problems of the length of the Interlachen from some movement on the with you :colon that because of the numbers for all practical purposes the final landing in another and call you gobble gobble the showed the kind of picture of the mutual numbers is not and so envisioned this that would have numbered in the huge number of the final set of candidacy and the group approximately meaning that for Fox he finds the group elements presented by Commission Japatul defined in practices vibration but but the order because the number of elements with the fail reaction the divided by the number of elements in the dangerous production Show in quarterly accounts also back up come out and Of course depends on the standard model every session was born in enterprise but in the case of the new they're all going to lose this is the proof is not your property group pocket defended his role computational and like almost all of them have computers the calmly combination of that and wife held in match 1st the again problem even for all groups regardless if all groups at 77 on such groups from only the most widely used property and signed for almost a certificate of those wouldn't be what happens in general is question whether isomorphic play according to the end of the century good nite simple question sojourn I think In the process of finding space in my mind gamma and Xray consider 2 and then I somewhat diminished somewhat preserving and commuting infection implies that Clinton wide open for John we just can't and that things were nice question of social and cultural again 2 major after once you you too go by but then the Nunavut who predicted that the the plant all that and also to it is with them all what was his name was hopeful that enterprise I equaled that of the guys wanted to produce keep forgetting his name on it that is came to align superior and and this kind of pot actually yeah feel the use much harder but when was on a senior executive senior science that is honest and victims of the much more elaborate broke ,comma what once were withdrawn that was generally calm and then extends to other groups on the part of the area now has recently been subgroups of Saudi it happened to 1 could expect a light hearted approved but not having much of traction said and is and I and many of the season this is this is the main about lock the action nation in microbiology and employment up concept comes from mind about that when and engineers smooth ride away and that up to the names of the men so it is because this is about blocking chairman equality if you think it'd be devotion to quality candidates from the fact that keep forgetting can Mexican and function in the medieval so people on the station and so you think about that as a pawn in the incident b so there .period numbers from front end of function points and it was just kind of people in government who is too simple reductions in certain contexts maybe sometime this month and we keep forgetting that Mexican think I was with my centerpiece of and a professor of political this the name but it's what you felt so supportive operated by accident but what is essentially a passion he signed it so it was just a point a defined point to better prevented from London opposition to the 1st of the form the is 1 of the things avoid them you may ask what of medical companies that compete for his courage and his coaches so what that meant and you might be thought about that last summer and then discourse on then reconstruction I had with a microbiologist with the news media about 30 years ago and when it's going to and there's is
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about 10 other names attached to these people are discovering that magic In fact and I think worst future something in the range and in and then this is a few could put that magic the was but that was some about somebody apparently found Smith himself was annoyed scores of families West Coast Entertainment just man the cement this and I somatic symptoms and the effects from the point of time medication the action the fastest time of the Isle of Wight Of course it's incredible that this is so much you might have to have high idea it also has interpretation the unity of how could so what what is this summit between them and that some of the projects they protectionism but what of the projected the demand "quotation mark when then the points in this when South Korea has run cost should summers so for at the time when I was in England this year we found school for what would be the 1st to some of this could why I mean there were some of life right and this and this may reduce some of computation communications from after constantly to what is called part of the moment and again the woman is a kind of remarkable met a mathematic discount by commuters who discovered the projected here in the management the French Camp demand for computer club the disease and the men from the boys number the problem cannot be prevented the In the case of alleged and that some of them in that means that could he is entropy might be on the phone with them and this enterprise was used by bye bye bye for now and so how about fight what would on the way which defined so you have to see all thing about MySpace's new that defense and the rebels nicely and the kickers .period increased pointing to speed of primary care the point is we I want to see just Mossman from implies the existence of quantum mechanics mathematics and and they're going to get out that here absolutely explains right statistics and the formula which came from just conformity move along large numbers the gunmen commodities that are sizzling language while lowlife numbers imply the existence of the she noted the normal law we kind of knew it was the 1st below the level legend that for me and however I was being said how you define enterprise in India UK you agreed so what so many of the fact that it's something you now trying to stop and they have some property in Latin and implementation of so what be this indicates all minutiae police said they would respect that the formerly phenomena in the form of quantum mechanics is just anything instead of specifying that it applies to prepare for and dimensional the spaces the instead the interventions space neighborhood of real or complex numbers makes any matter I want to see what in this particular case if you know it for use of condoms so instead of that it would be space and you want to do something like this but what he would be matters of substance such space and and to go to each subsequent want the number of despair and the condition of a deterioration in the 2 trade I thought this up and the whole thing and of course you need to have the notion of a person on the way to do it follows it was very positive about the differences in the way you look at the properties is only 1 solution a solution following the Dec . 2 4 that for the race be himself idea if you want to know is that this fall and this should be a man of his recall in physical danger to Americans and use the company's respectability In the process is complete that is the point of being admitted mistakes well units aspirations and stated that kind and this would be in the months and this is an issue but it wouldn't a good thing was that would be pretty the point is to appeal to the fact that can I use your credit United European audience of course all formerly in the space of just for of With the waters so the essential essential property this energy industry said before according to property of the akin the property of the presidential measures the integration of the get a fundamental extension of a future of the opinion of some so what do you do that and then to approve that of course there may even if you finish the end of the object that black people can match up with a better plan opponent for many space the points that included the following week but some of the universe could secure this is .period ematical vocal being estimated and and then in in particular have not been winning station of the onethird of the taken from frame a frame and some foreign it doesn't right In the 2nd or the United States Japan's does depend debate the city is surrounded about this and future plans can become part of the new raising and the number is much more than in his usual usual usually 3 or 4 years so so what would be ended and for the moment defiance and so have I got to consider again said this will be a waste to dialog it just the bank analyzed becomes a prime space and they can't me and want to prove you want and you want approved the basic properties of the standard according to the report which stated that the that and that the government computers the best thing that's not completely on so let me assure you the kind of language from the so the
1:47:37
point is that in quantum mechanics and it just feels in In mathematics the going to be consistent use most of it in the good guys believe that my our belief system you make a mess Wallace but in quantity Connecticut doesn't quite big system was not hubris examples of plastic the success of the company the Small Business reductions in quantum mechanics at sporting thing to support the cause this morning on behalf of the space of functional and it would be sensible and then the and this kind of physically has some meaning that you could call the quantum Universal did you do but given the huge campaign immediately ,comma isolated quantum mechanics that thing that by physical with his Wimbledon before this was like a mean actually remember we had that in mind is that Parliament because the space required additional structure and could you could get the of functions would intimidate those spaces in which particular functional allowed lot projection with this principle he not all of which you can do it again 2 pro the state that all year distribution basically group England Spain but I thought information they can apply for additional functions in this
1:49:35
systematic work happens in the world and urging and then Of all the famous production classical case because we have lunch and you want a project this projection prohibit quantummechanical however managed group actually producing them in the oldest if you shouldn't become constantly and that would help but you can go from 1 to another former become become so "quotation mark "quotation mark I think we can ask about equality when applied and kissed basic quality he was ruled by violence in the way How and then became an image if you look what happened in this example in classic example becomes according and he conditions amusing but why they use the problem not the difficult not only because it is too early to build was it was brought in the conjecture was made from formulated different the only thing that I want to use the language but In the face of what the source of employment conditions the latter conjecture and needed before going on to the sentry in like the head at the quality and he wanted to In the offices here is no more but this was just ability a terrible usable although there many components some comported going multiples undergoing multiple multiple completed its opulent Europe the useful presentation 1 thing appears mainly that this would happen in this example and that you can that too many changes and different picture and that it was cool 5 years by way the good sky and the history of conditions that would make and had to walk in 1 way to the is exactly along the slightest just you have to get used entered the same way you to fall for the world you you have to respect and were usually you would like to make a
1:52:26
story of power went on again the standard number in the numbers just sat on everything from industry in again with a long life because combined emerge from this quite good kind of annoying for which means that in the middle and upper half of the population it would have the following here you have a homogeneous from being proportional to the number original formalized equal and projections such a defiant projection means that the whole musical the substrates were mentioned from in the and this is a political point which makes up the flattered however however if you just assume that you are all before and after quite Jr and then become kind of apology this same way in for as far as floor 4 per cent to 4 different but you competition of obviously equal the only thing that did to check the this this operation is separate from survival guide he this with what was important in classical that not only because it would still publishing it through for more fees would quite good images and he also we have to show he can go but this guy is kind of what we have to say exactly what it takes a couple of pages on about the initial not what we now call it might extend back shore the term later but the whole of convection Petito economic function as their counterparts in in in fall for operators In a different kind of of stable and that the product which have of been developed kind of thing it interesting enough nothing Arkansas the end of the story about the few them