http://qs1969.pair.com?node_id=203798


in reply to Re: What is zero divided by zero anyway?
in thread What is zero divided by zero anyway?

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 non-denumerable infinities (memory gets fuzzy here): the power set (set of all subsets) of N is non-denumerable; and the set of real numbers is also non-denumerable -- 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?
"Sidney Morgenbesser"