Re: Cardnality of integers > Cardnality of integers

On 2008-03-14, S_Paske@xxxxxxxxxxx <S_Paske@xxxxxxxxxxx> wrote:
Suppose one were to construct a list of integers using this method:

1 = 2^0 * 3^0 * 5^0 * 7^0...
2 = 2^1 * 3^0 * 5^0 * 7^0...
3 = 2^0 * 3^1 * 5^0 * 7^0...
...

Once someone has completed the list of all of the integers, it seems i
can use the same diagnoalization argument to show that there is an
integer not in the list.

In the diagonalization of the reals, every infinite sequence of digits
represents a real number.

How do you prove that what you end up with in your case is an integer?
It's an infinite product, and infinite products are only defined where
a suitable limit exists.


- Tim
.