Liar Paradox

Does "Liar Paradox" requires this crappy Axiom of Infinity, that "for all N there exit N+1 > N"?
Because if you don't believe Axiom of Infinity, then for some theory (or program) N, you can't construct it's Liar structure, as it would require more memory than you have physically.

Of course, jews would say, that without infinity there is no mathematics, but why do we need this jewish tendency toward abstraction and casuistry anyway? Can you show us practical usefulness of your deceptive regilious theories, jews?

there exists
self fix

>>1
Enjoy living in modulo N.

>>3
Enjoy your living under a stone.

And we have this "big-bang theory" now, that states that Universe expands and implodes "modulo N", lol.

>>1
VIPPERS

Greeks thought earth was an infinite flat plane and there can be parallel lines. Today every child knows that earth is round, but some "god chosen" jews still believe in parallel infinite long lines.

>>1
Can you show us practical usefulness of [infinity]
Everything that has ever used maths? If you discard this axiom, you don't even "believe" in the naturals, so all of mathematics is lost.

>>7
>Everything that has ever used maths?
practical usefulness

>If you discard this axiom, you don't even "believe" in the naturals, so all of mathematics is lost.
If you need natural, you're probably doing something, building yet another crazy theory with half-dead cats in perpetual motion.

>>8
if you need naturals
self fix

>>9
doing somethin wrong
another fix

>>10
Just... stop.

>>8,9
With what do you replace naturals, with gays?

>>8
Calculus is used in many, many applied fields. There's no argument to be had here; unless you're secluded from society in a shack you built yourself, magically beaming posts to this board, you are already reaping the practical benefits of maths.

>>1-9000

gay vergins

>>13
Where exactily (outside of vague natual language) it is used? Can you show us concrete computer program that works with "infinitesimals"?

>>12
Why not use LISP's lists, limited by memory amount of computer, LISP-system runs on?

>>1
jews?

JEWS

>>15
Every inductive proof ever.

>>17
Proof that uses infinity to prove infinity? Looks like a pseudoscience. BTW, how can I prove that math isnt a religious pseudoscience?

>>16
Yes. Jews like math, because of some traditional numerology practices related to their crazy religion and infinity, as I heard.

>>18
..and it looks like OP threw in the towel. Argument over.

thread.close();

>>20
Why not use this.close you JEWS?

import threading
thread.__over__()

>>22
ONE WORD: THE FORCED INDENTATION OF THREAD OVER. THREAD OVER.

So the math is a useless pseudoscience I guess.
LISP is much, much better than math.
And LISP has nice uniform syntax, without all these greek and jewish letters.

Also, I easily copy-paste LISP code. But mathematics requires ugly La-TeX stuff to graph crazy diagrams.

Even SEPPLES has more rigor and elegancy than mathematics.

google 'lazy lists'

uh

OP is an idiot

one of the most prolific finitists right now is jewish

Lisp is infinite. This is the Lisp paradox.

http://try.rakudo.org/
my @fibs := 0,1,*+* ... *; say @fibs[7];

Inf <3.

>>28
You don't know what "jewish" means. It is not nationality or race. It is more like ideology, being arrogant and "God Chosen", worshiping infinity and the stuff.

>>27>>30
recurision != infinity

>>30
Perl
Now you have infinite problems.

>>32
Please optimize your quoting !

>>30
0,1,*+* ... *;
Perl has a special syntax case just for fibonacci sequence?

Please, introduce Larry Wall to this wiki article:
http://en.wikipedia.org/wiki/Bloated

>>35
Perl has a special syntax for everything!

>>36
For what purpose?

>>37
http://en.wikipedia.org/wiki/Bloated

I can do the same in my Lisp+Refal dialect, using simple function

foldS a b o -> [a b].{[a b]=>seq a [b o,a,b].rec}
foldS 0 1 `+`
(0                               1                             
 1                               2                             
 3                               5                             
 8                               13                            
 21                              34                            
 55                              89                            
 144                             233                           
 377                             610                           
 987                             1597                          
 2584                            4181                          
 6765                            10946                         
 17711                           28657                         
 46368                           75025                         
 121393                          196418                        
 317811                          514229                        
 832040                          1346269                       
 2178309                         3524578                       
 5702887                         9227465                       
 14930352                        24157817                      
 39088169                        63245986                      
 102334155                       165580141                     
 267914296                       433494437                     
 701408733                       1134903170                    
 1836311903                      2971215073                    
 4807526976                      7778742049                    
 12586269025                     20365011074                   
 32951280099                     53316291173                   
 86267571272                     139583862445                  
 225851433717                    365435296162                  
 591286729879                    956722026041                  
 1548008755920                   2504730781961                 
 4052739537881                   6557470319842                 
 10610209857723                  17167680177565                
 27777890035288                  44945570212853                
 72723460248141                  117669030460994               
 190392490709135                 308061521170129               
 498454011879264                 806515533049393               
 1304969544928657                2111485077978050              
 3416454622906707                5527939700884757              
 8944394323791464                14472334024676221             
 23416728348467685               37889062373143906             
 61305790721611591               99194853094755497             
 160500643816367088              259695496911122585            
 420196140727489673              679891637638612258            
 1100087778366101931             1779979416004714189           
 2880067194370816120             4660046610375530309           
 7540113804746346429             12200160415121876738          
 19740274219868223167            31940434634990099905          
 51680708854858323072            83621143489848422977          
 135301852344706746049           218922995834555169026         
 354224848179261915075           573147844013817084101         
 927372692193078999176           1500520536206896083277        
 2427893228399975082453          3928413764606871165730        
 6356306993006846248183          10284720757613717413913       
 16641027750620563662096         26925748508234281076009       
 43566776258854844738105         70492524767089125814114       
 114059301025943970552219        184551825793033096366333      
 298611126818977066918552        483162952612010163284885      
 781774079430987230203437        1264937032042997393488322     
 2046711111473984623691759       3311648143516982017180081     
 5358359254990966640871840       8670007398507948658051921     
 14028366653498915298923761      22698374052006863956975682    
 36726740705505779255899443      59425114757512643212875125    
 96151855463018422468774568      155576970220531065681649693   
 251728825683549488150424261     407305795904080553832073954   
 659034621587630041982498215     1066340417491710595814572169  
 1725375039079340637797070384    2791715456571051233611642553  
 4517090495650391871408712937    7308805952221443105020355490  
 11825896447871834976429068427   19134702400093278081449423917 
 30960598847965113057878492344   50095301248058391139327916261 
 81055900096023504197206408605   131151201344081895336534324866
 212207101440105399533740733471  343358302784187294870275058337
 555565404224292694404015791808  898923707008479989274290850145
 1454489111232772683678306641953 2353412818241252672952597492098
 3807901929474025356630904134051 6161314747715278029583501626149 ...)

>>33
Now I have hyper-lazy-meta-infinite problems, thank you very much.

>>35
That is general syntax. Larry got on a Huffman coding kick, and the result is just about any conceptually simple expression is equivalent in length to the J version fairly tight.

>>40
JEWS version

Haven't you already made 2 threads to troll about this? Stop it already.
Even if our world may be finite at the fundamental level, one will use infinities to reason about many practical things. Just like one uses integrals, derivatives, induction, complex numbers, matricies, groups, and so on... to reason about both abstract and real things. You wouldn't have modern physics, electornics, and most things relying on hard sciences today without math. Let's take a simple example everyone would understand: A rectangle with a side of length one is given, the diagonal's length is square root of 2 (given pythagora's theorem). The square root of 2 is an irrational number (easily proven), thus its decimal representation is infinite and no fraction may give you its value (but you can get approximations, as in sqrt(2)-approx<e, where e is sufficiently small value representing the error that can be tolerated). Now if you were to draw such a rectangle in the real world and calculate the diagona's distance, you would get such a value that approximates sqrt(2) to a given degree. The error would depend on the granularity of the thing you used to do your measurements with. Given a smaller scale, you would get better approximations. For an infinitely small granularity, you would reach sqrt(2), or you could say that as the granularity approaches 0, the value of the length approaches sqrt(2) - the concept of limit.

Our world's discrete nature does not mean we cannot use math to obtain incredibly important results. Math can be used to analyze systems which have infinities in them, but it can also be used to deal with completly discrete systems.

If you don't want to come to terms with this, enjoy your ignorance.

>>41
I said J, not Haskell.

>>42
YHBT.

>>42
>one will use infinities to reason about many practical things.
Sorry. Cant see, how your "infinites" help wth practical things. You probably hallutinate or something.

>You wouldn't have modern physics, electornics, and most things relying on hard sciences today without math.
Yeah! We would have better sciences, without all that religious jewish crap.

>Let's take a simple example everyone would understand: A rectangle with a side of length
please, define "length" or GTFO, you crazy jewish sophist!

Mathematics would certainly have not come into existence if one had known from the beginning that there was in nature no exactly straight line, no actual circle, no absolute magnitude. -- Friedrich Nietzsche

If a `religion' is defined to be a system of ideas that contains unprovable statements, then Godel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one. -- John D. Barrow, Between Inner Space and Outer Space, Oxford University Press, 1999, p 88.

A religion is usualyl based on blind acceptance of some propositions.
Math is not based on blind acceptance of any propositions, it merely tells you how hypothethical (and real) systems behave.
If you can't understand the distinction, the foundations on which you reason are broken.

>>47
A math is usualyl based on blind acceptance of some propositions.
Religion is not based on blind acceptance of any propositions, it merely tells you what will happen hypothethical (and real) to your eternal soul.

Many scientists are deeply religious in one way or another, but all of them have a certain rather peculiar faith – they have a faith in the underlying simplicity of nature; a belief that nature is, after all, comprehensible and that one should strive to understand it as much as we can. Now this faith in simplicity, that there are simple rules – a few elementary particles, a few quantum rules to explain the structure of the world – is completely irrational and completely unjustifiable. It is therefore a religion. -- Sheldon Glashow, The Quantum Universe, co-produced by WETA-TV and The Smithsonian Institution, 1990.

Suppose we loosely define a religion as any discipline whose foundations rest on an element of faith, irrespective of any element of reason which may be present. [Atheism], for example, would be a religion under this definition. But mathematics would hold the unique position of being the only branch of theology possessing a rigorous demonstration of the fact that it should be so classified. -- H. Eves, Mathematical Circles, Boston: Prindle, Weber and Schmidt, 1969.

>>49
Belief in comprehensible world is rational because WE EXIST. Worlds with irrational rules would make it less likely for life to appear, much less intelligent life.
It should also be observed, that our mind itself was evolved in such a way that we are to find patterns and correlations in the natural world. If the world would not be comprehensible, intelligence would not likely evolve, and would probably be pointless.

>>51
Falls to the anthropic principle. It could be just a freak event of chance.

>>52
The sheer consistency of all the natural laws we've been able to derive and test says otherwise. We constantly keep finding the world more and more consistent, not less.

http://www.tenthdimension.com/
http://imaginingthetenthdimension.blogspot.com/
http://www.youtube.com/user/10thdim

>>51
please, define "EXIST"

for me "exist" if just a synonym of "observable by my senses". That is the object is just its perception.

>It should also be observed, that our mind itself was evolved in such a way that we are to find patterns and correlations in the natural world.
So, if I subjectively find that "infinity" is an ugly and nonsensical "pattern", then so finds evolutution? Nice, Plato! You just disproved your whole spiritual mathematical world!

>>55
Why do you keep going on and on about it? Infinity may not exist in our space, but it can exist in abstract systems just fine. Why do you have such a hard time dealing with it? Is it really that hard to understand for you? Are you having trouble understanding hypothethical? What about understanding why someone would invent negative numbers or complex numbers even if their meaning is not related to the real world, however they can be used as intermediaries in solving problems... Argh, why do I even bother responding to your posts. If you don't know math, you don't understand sciences either. If you actually tried to limit yourself to a very tight subset of math without using the rest of math to help you along (while still staying well within the confines of your system), you won't get very far.

>>56
God may not exist in our space, but it can exist in abstract systems just fine.

>>56
>If you actually tried to limit yourself to a very tight subset of math without using the rest of math to help you along (while still staying well within the confines of your system), you won't get very far.
I'm using LISP and don't have need for math at all. Where is your God now?

>>57
Sure, if you can define what ``God'' is, one can easily imagine a system where it would be logical for such an entity's existence. It doesn't mean such an abstract system has any bearing on our reality.

Richard Phillips Feynman (May 11, 1918 – February 15, 1988) was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics. For his contributions to the development of quantum electrodynamics, Feynman received the Nobel Prize in Physics in 1965. During his lifetime, Feynman became one of the best-known scientists in the world.

Feynman believed, that existence of a God is a "consistent possibility": "A young man, brought up in a religious family, studies a science, and as a result he comes to doubt – and perhaps later to disbelieve in – his father's God. Now, this is not an isolated example; it happens time and time again. This young man has learned a little bit and thinks he knows it all, but soon he will grow out of this sophomoric sophistication and come to realize that the world is more complicated, and he will begin again to understand that there must be a God. This young man really doesn't understand science correctly. I do not believe that science can disprove the existence of God; I think that is impossible.  And if it is impossible, is not a belief in science and in a God – an ordinary God of religion — a consistent possibility?"

Out of context quote mining sure is great Mr. finite troll?

>>59
Just after you define what "infinity" and "infinite set" are.

>>61
While Newton's fame came from his work in the field of science, his work on Biblical hermeneutics was the work he most loved. He also wrote many works that would now be classified as occult studies. Newton wrote a number of religious tracts dealing with the literal interpretation of the Bible, as he considered himself to be one of a select group of individuals who were specially chosen by God for the task of understanding Biblical scripture. Newton’s conception of the physical world provided a stable model of the natural world that would reinforce stability and harmony in the civic world. Newton saw a monotheistic God as the masterful creator whose existence could not be denied in the face of the grandeur of all creation.

Descartes claimed to be a devout Roman Catholic, claiming that one of the purposes of the Meditations was to defend the Christian faith. Stephen Gaukroger's biography of Descartes reports that "he had a deep religious faith as a Catholic, which he retained to his dying day, along with a resolute, passionate desire to discover the truth." After Descartes died in Sweden, Queen Christina abdicated her throne to convert to Roman Catholicism (Swedish law required a Protestant ruler.) The only Roman Catholic she had prolonged contact with was Descartes, who was her personal tutor.

Pascal believed that even if the existence of God cannot be determined through reason, a person should wager as though God exists, because living life accordingly has everything to gain, and nothing to lose. It was set out in note 233 of his Pensées, a posthumously published collection of notes made by Pascal in his last years as he worked on a treatise on Christian apologetics. Pascal's Wager was groundbreaking as it had charted new territory in probability theory, was one of the first attempts to make use of the concept of infinity.

Gödel was a convinced theist. He believed firmly in an afterlife, stating: "I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife. My belief is theistic, not pantheistic, following Leibniz rather than Spinoza." He said about Islam: "I like Islam: it is a consistent idea of religion and open-minded."

So we're trolling Xarn, basically?

>>67
Fuck you.

ああ～Xarnさま～