[SOLVED] Frivolous theorem of arithmetic on Wikipediaby Icebreaker Tags: arithmetic, frivolous, solved, theorem, wikipedia 

#19
Apr1005, 06:16 AM

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Perhaps Wikipedia needs a section of "The most false theorems" as well:
Here's mine: The primes are closed under multiplication.. 



#20
Apr1005, 09:03 AM

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Zurtex,[itex] 1+1=2 [/itex] is an equality,not an equation...
Daniel. 



#21
Apr1005, 11:37 AM

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But the real problem with the page is not that the theorem is useless, it's that the page is. The page provides no useful information at all; it doesn't explain why the theorem is true or what its significance is. If you already know the theorem then the page doesn't tell you anything new or interesting. And if you don't know the theorem then you aren't going to learn anything from the useless remarks on the page. 


#22
Apr1005, 01:19 PM

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The page can be updated, modified; information can be added. Why don't you go add something to the page instead of deleting it altogether?




#23
Apr1005, 02:06 PM

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#24
Apr1005, 02:20 PM

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There's an interesting interpretation of this theorem in the context of a nonstandard model:
Most natural numbers are external  here, that means they're bigger than any natural number we can "get" to. (i.e. as long as we stay in the word of natural numbers, doing anything imaginable with internal numbers will never produce an external number) 



#25
Apr1005, 03:21 PM

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#26
Apr1005, 03:31 PM

P: 678





#27
Apr1005, 04:34 PM

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I found the equivalent MathWorld page quite enlightening when I came across it. 



#28
Apr1005, 06:01 PM

P: 678




#29
Apr1005, 06:18 PM

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Are you implying that the theorem is not useful?




#30
Apr1005, 06:20 PM

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I put this theorem into the class of things everybody knows, but few actually realize until they have it pointed out to them. There are lots of such facts... for instance, once I saw the example of a nonzero function whose taylor series was zero, it took me several years before it dawned on me that most infinitely differentiable functions are not analytic. But, if at any point, someone had stated that fact to me, my reaction would've been "Oh right, that's obvious!"




#31
Apr1005, 06:33 PM

P: 678





#32
Apr1105, 04:50 PM

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Yeah yeah I know, some times I take things too seriously, I've edited the front page, please edit anything I've wrote if you can think of something better.



#33
Apr1405, 12:33 PM

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I remember it being proven by someone "jokingly" a while back on one of the threads. That proof is much more simple, iirc.



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