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mitsy
United States1792 Posts
the verb is _constitutes_. i would say that for something to be proven it need be consistent with other already proven things. but is "being proven" ever more than a perception, and is our set of "already proven things", even if it is the largest possible set of things that are consistent with eachother, necessarily "truer" than a smaller set? "what do we mean by proof" is a slightly different question, kind of like "what convinces us that something is proven?" | ||
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PlayJunior
Armenia833 Posts
On November 16 2005 01:10 mitsy wrote: well i may have not answered the right question earlier in this thread. the verb is _constitutes_. i would say that for something to be proven it need be consistent with other already proven things. but is "being proven" ever more than a perception, and is our set of "already proven things", even if it is the largest possible set of things that are consistent with eachother, necessarily "truer" than a smaller set? "what do we mean by proof" is a slightly different question, kind of like "what convinces us that something is proven?" I didn't understand the middle paragraph. Once more pls  | ||
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Chibi[OWNS]
United Kingdom10597 Posts
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Alan Schezar
France44 Posts
On November 12 2005 23:30 HeadBangaa wrote: It simply means that S cannot be ordinary in the first place. It's an extraordinary set that contains all ordinary sets. This example does illustrate some of the seemingly strange characteristics of set theory. Like that one about successive power sets of the empty set: A power set of S, P(S), is the set of all subsets of S. if S = (a, b, c) P(S) = {a, b, c, {a,b}, {a,c}, {b,c}, {a,b,c}} (I think I'm missing one element, but you get the point) The empty set, Ø, contains nothing. It's "null space". Ø = {}. But... P(Ø) = {Ø} P({Ø}) = {Ø, {Ø}} P({Ø, {Ø}}) = {Ø, {Ø}, {Ø, {Ø}}, {{Ø}}} etc... I think that's freakin weird and it has no actual application that I can think of. Oh my that's great intution you have here ^^ in fact recursively it's the formal creation of the natural numbers ! (math freak ftw) 0 = Ø 1 = Ø, {Ø} 2 = Ø, {Ø}, {Ø,{Ø}} 3 = Ø, {Ø}, {Ø,{Ø}}, {{Ø}} ..... if you like it you could read some math-theory books and if you don't already read those you might like it (no joke) Godel and Hilbert worked on this kind of theories, Hilbert whos was very skilled with proof by absurd. exemple : let's have x1,x2,x3,x4,x5 (like1a2a3a4a5a) and you know that the total sum isn't null prove that there are 3 xi ( "i" in {1,2,3,4,5} ) that their sum isn't null either. Answer later ^_^ | ||
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LastWish
2015 Posts
People seek these rules(like axioms) and want to determine the world around us on the base of deductions and proofs. But what if this world is based on indefinite number of rules? Then we will never know how it works since humans seem to only work with definite knowledge. We will only know the piece of cake, but never taste the real truth. | ||
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sundance
Slovakia3201 Posts
On November 12 2005 22:02 BigBalls wrote: speaking of set theory, this reminds me of extraordinary sets. a set is extraordinary if it contains itself. For example, A = {1,2,3,A} is extraordinary. Define S to be the set that contains all ordinary sets and nothing else. Suppose S is ordinary. Then S contains itself because it contains all ordinary sets, which makes it extraordinary, which is a contradiction. Now suppose S is extraordinary. That means it contains itself. But S contains nothing but extraordinary sets, so it cannot contain itself. Another contradiction. That's why we have system of sets and not set of sets. How it work in physic: Someone come up with some new theory as a answers to some experimentali showed contradiction of current theory.Then he compute results of some experiments using his new theory (usually it's expanded current theory).Then if numbers are equal with numbers from experiment and it survive every other attempt(read as a some insane experiment) of another smart-ass it's considered as "we don't have any evidence why we should consider it as an another bullshit usless theory so we can say (DISCLAIMER : we don't provide warranty of any kind) it's true and we will give Nobel prize to this lucky bastard". That's the problem with super-strings theory b/c it works in cases when we are able to make computation but there are many computations that nobody can currently do.But where we can it works super fine. But my English is super newbie so i really don't know if it's even uderstable.I can explain it in slovak but in english it's very hard for my and that's why i don't post in general forum. | ||
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