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Re: Re: What is zero divided by zero anyway?by arturo (Vicar) 
on Oct 08, 2002 at 23:49 UTC ( #203798=note: print w/replies, xml )  Need Help?? 
Not only that, but "infinity" doesn't name one number. There are different infinities ... For example, the set of natural numbers (0,1,2,3,...), aka N, is a *denumerable* infinity ('denumerable' meaning, 'can be put in a 1:1 correspondence with the members of N'  so N satisfies this definition trivially), as is the set of multiples of 10  EVEN THOUGH that set is a subset of N. The set of multiples of 10 is, intuitively, a tenth the size of N? But no, for every member of the set of multiples of 10, you can find a partner in N. Moreover, there are nondenumerable infinities (memory gets fuzzy here): the power set (set of all subsets) of N is nondenumerable; and the set of real numbers is also nondenumerable  there are too many points on the real line to put in a 1:1 correspondence with N (intuitively: though with the case of multiples of 10, there is a way to figure out what the next number is, there's no way to find the "next point" given a specific point on the real line). Isn't math fun? If not P, what? Q maybe?
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