Re: Galileo's Paradox

On 11/29/2006 7:36 PM, Tony Orlow wrote:
Eckard Blumschein wrote:
On 11/29/2006 3:58 PM, Tony Orlow wrote:
where one set contains all the
elements of another, plus more, it can rightfully be considered a larger
set.

All of oo?



Yes. All of the naturals are integers. Only half of all the integers are
naturals.

All of the points in (0,1] are in (0,2], but only half of all of the
points in (0,2] are in (0,1].

You are equating two quite different notions: smaller and half as large.
In case of two finite heaps of size a and b of numbers, a=b/2 implies a<b.
In case of a=oo and b=oo, we may have a=b/2 while a is not smaller than
b but simply not comparable: oo = oo/2.

.

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