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Hi,

I apologize for my total ignorance in the sphere of mathematics and the possibly very silly question I'm about to ask. My mathematical knowledge level is quite limited (pretty much finished with some slightly more advanced stuff then grade 12) so please if possible limit too much terminology to about that level 12 math. Again I don't mean to offend anyone & I'm sorry if the following sounds like a joke but I am genuinely interested and cannot quite grasp the reason for it.

I've been curious for quite sometime now, What is the significance for a mathematics to frequently require proof for both finite & infinite cases of theorems ? Why isn't it satisfactory to proof any theorem for a reasonably high finite x (whatever x is - be it set of some numbers) ? The reason why I'm asking is that in real-life applications (not talking about software application but life applications like count a bag of money or something like that) there is likely never need to deal with infinite of anything really - it might be a very high quantity but never infinite. So why does mathematics need and requires proof for infinite case as well instead being satisfied if finite case ?

Thanks for any advise!!

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6 
 @mikiyfi: this is a site for research level math questions, hence your question is off-topic here. (Please see the FAQ for more details.) But it would be appropriate at math.stackexchange.com, and I invite you to repost it there. – Pete L. Clark Jan 29 2011 at 3:37
What Pete said. – Amit Kumar Gupta Jan 29 2011 at 3:38
6 
 They're going to close your question, but I'll try to say something short and useful. In many situations, the infinite is easier to analyze than large finite quantities. Thinks of water or air: understanding the interactions of astronomical numbers of particles seems hopeless, but view these substances as fluids gives rise to tractable mathematics. The same thing happens in pure mathematics - on the infinitely long view spurious fluctuations vanish and simple basic laws emerge, for example the prime number theory, or the central limit theorem and normal distribution. – David Feldman Jan 29 2011 at 3:46
1 
 mikiyfi -- the problem is that your question as it is stated isn't precise enough to admit an answer either here or on math.stackexchange.com. But let me comment: consider the following "theorem": every real $x$ is less than $2^{100}$. $2^{100}$ is a ridiculously large number for most practical purposes, it is much larger than the age of the universe measured in seconds or even its life expectancy, I believe. And the theorem is true for all $x<2^{100}$, but it fails for $2^{100}+1$. So proving that something is true for a reasonably high real $x$ does not prove it for all real $x$. – algori Jan 29 2011 at 3:59
1 
 algori, thanks for comments. This is exactly what I'm interested in if 2 to the power 100 is so large it will likely never be used hence it's not important ... or maybe I'm wrong:) – mikiyfi Jan 29 2011 at 4:04
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closed as off topic by Pete L. Clark, Willie Wong, Mariano Suárez-Alvarez, Andres Caicedo, David Hansen Jan 29 2011 at 4:08

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