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06022013, 04:11 PM  #21 
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I mean infinity...I can't spell

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06022013, 04:13 PM  #22 
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I think it is more like saying that 1 is the largest number, which is not true. It's clear the conclusion is wrong, but all the ideas leading up to that conclusion seem true. So, is logic unreliable?

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06022013, 04:24 PM  #23  
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You cannot both say that L=L^2 and L^2/L=L simply because if L is the largest real number L^2 (which we should then treat as infinity^2)=L so therefore this step should read that L>=L 

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06022013, 04:38 PM  #24  
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If I postulate a "largest real number", then it must have the property of being greater than its own square. Mathematicians think such an assumption is nonsense. But in philosophy, this kind of assumption is made in the ontological argument for god. I'm surprised philosophers don't dismiss it as well. i.e. the ontological argument goes something like this. Imagine a most perfect being. Does this being exist? Yes, it must have the attribute of existence, otherwise we've not imagine the most perfect being. Hence, god exists. p.s. Seems the arguments flaw is the assumption that a largest real number exists. Because such a number would have to be bigger than it's own square. 

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06022013, 04:39 PM  #25  
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06022013, 04:41 PM  #26 
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06022013, 04:51 PM  #27  
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It's math, that's what's wrong.
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06022013, 05:02 PM  #28 
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The technological world we thrive in today is thanks to the scientists and engineers who use math everyday
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06022013, 05:04 PM  #29 
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LeeD doesn't care about technology. He likes to play sports outdoors and be One with Nature.

06022013, 05:08 PM  #30  
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Very true! 

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06032013, 07:09 AM  #31 
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Eddy, I just realized that there seems to be no direct way to generate the next prime number, given the previous one, except through various "sieve" schemes which actually just list possible candidates and eliminate the composite ones. In other words, given 7, there seems to be no direct way to find that 11 is the next prime number.
Has it been proven to be impossible? Not easy to find the answer from Google. Such a simple problem and no known solution! 
06032013, 05:29 PM  #32  
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06032013, 06:40 PM  #33  
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06032013, 08:14 PM  #34 
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There is a proof that it cannot be done. On page 38 it says, "...they produce values of Y divisible by p, contradicting the hypothesis. Hence, no such prime producing polynomial exists.

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06032013, 08:29 PM  #35 
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Here's a mindblowing fact.
There are infinitely many natural numbers, and infinitely many real numbers, right? Well it turns out that the infinity of the real numbers is larger than the infinity of the natural numbers! To be mathematically precise, what this means is that there is no function from N > R that is bijective. In other words, no onetoone correspondence. But get this. It just so happens that there as many rational numbers as natural numbers, and in fact, just as many integers as natural numbers! In mathematics, we call this the cardinality of a set. For finite sets, the cardinality is simply the number of elements but for infinite sets it gets more interesting, and what cantor showed is that N < R. It has long been conjectured that there is no set S, such that N < S < R. This was known as the continuum hypothesis. However, it won't ever be settled. Kurt Godel and Paul Cohen proved that the continuum hypothesis cannot be proven from the axioms of modern mathematics. 
06042013, 09:37 AM  #36  
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Do you know about infinities higher than R? I think there is one for the number of curves in 2D space? Probably 2 more infinities higher than R? 

06042013, 01:25 PM  #37  
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Proof: It suffices to show that no function f: S > P(S) can be surjective. Let A be the set of all elements x in S such that x is not in f(x). Then if x is in A, x is not in f(x), and so f(x) \= A. If x is not in A, then x is in f(x) \= A. Therefore, no element can get mapped to A, so f is not surjective. Last edited by Claudius; 06042013 at 02:21 PM. 

06042013, 01:39 PM  #38  
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What about the infinity of curves you can draw in a plane? Is it the same one as R? 

06042013, 02:26 PM  #39  
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The set of points in the plane will have the same cardinality as R, same with the set of curves. 

06042013, 06:53 PM  #40 
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