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Is infinity even or odd?by Icebreaker
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#1
Feb2805, 06:41 PM

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Is infinity even or odd? If it's even (or both), then it would mean there's a finitely largest prime.
By coarsely applying limit concepts, and lim(x>inf)x/2 does not yield a remainder. 


#2
Feb2805, 07:03 PM

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I'm no math Phd, but I do know this: infinity is not a number!



#4
Feb2805, 08:08 PM

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Is infinity even or odd?
So, what, we can assume that there will ALWAYS be larger primes?



#5
Feb2805, 08:12 PM

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You shouldn't assume anything in math. I seem to remember seeing a proof of that somewhere, but I can't remember any of the details. My memory could be wrong. Surely somebody will know though...



#6
Feb2805, 08:26 PM

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Suppose there are finitely many primes. Can you find a number divisible by all of them? Can you find a number not divisible by any of them?



#7
Feb2805, 08:45 PM

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Interesting. Is hydrogen male or female? The answer is similar.



#8
Feb2805, 09:00 PM

P: n/a




#9
Feb2805, 09:07 PM

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#10
Feb2805, 11:49 PM

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infinity = 2 times infinity, hence infinity is even, which may seem odd.



#11
Mar105, 12:50 AM

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It's even odder since infinity=2*infinity+1, hence it's odd as well as even. (joking )
Seriously though, infinity is not a number that you can perform arithmetic with. You can add it to the reals and make what's often called the extended reals, but don't expect it to play nice with the rest of the numbers. Certainly don't expect it to have any nice properties like even or odd. 


#12
Mar105, 10:36 AM

P: n/a




#13
Mar105, 10:53 AM

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Not every number can be formed from a product if primes if there were only a finite number of them: multipply them all together and add 1.



#14
Mar105, 10:58 AM

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Suppose their are finitely many primes, [itex]p_1,p_2,\ldots,p_n[/itex]. Then consider their product [itex]M=p_{1}p_{2}\ldots p_{n}[/itex]. Then M is divisible by all the primes. This answers Hurkyl's first question (from post#6). Can you use it to answer the second? edit:I type slower than matt! 


#15
Mar305, 04:36 AM

P: 1,603

See http://www.physicsforums.com/showthr...006#post478006 Any thoughts on this subject anyone? If an infinite integer is allowed, then it must also have an infinite number of digits, right? 


#16
Mar305, 04:42 AM

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They aren't elements of [tex]\mathbb{Z}[/tex] or [tex]\mathbb{N}[/tex] by definition so your argument is baseless.
You are saying: if we assume that when cantor said the natural numbers he actually meant something entirely different then his argument is wrong. As he didn't mean something entirely different his argument is correct and you are wrong. 


#17
Mar305, 04:51 AM

P: n/a

infinity is a description not a numerical value and since only numerical values can be odd or even, infinity is neither.



#18
Mar905, 12:41 PM

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Is green even or odd? Is salt even or odd? Is Fred even or odd? (Oops, bad example, Fred is definitely odd!)
The point is that "infinity" is not a member of the set of integers and that is all the terms "even" or "odd" (in the mathematical sense) apply to. 


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