Re: Cantor Confusion
- From: David Marcus <DavidMarcus@xxxxxxxxxxxxxx>
- Date: Thu, 2 Nov 2006 04:25:32 -0500
mueckenh@xxxxxxxxxxxxxxxxx wrote:
The diagonal is an infinite sequence. So the diagonal is longer than
any of the finite sequences. But the diagonal consists of elements of
the finite sequences. So it cannot be longer than the maximum of the
finite sequences. If this maximum does not exist, you cannot take the
supremum omega for it, because the supremum is not a member of the
sequences and does not supply elements of the diagonal.
Let's try a simpler problem. Consider the following list.
1
1
1
....
In other words, consider the sequence x where x(n) = 1 for n a natural
number. How long is this sequence?
--
David Marcus
.
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