Re: A consideration concerning the diagonal argument of G. Cantor

On 2008-05-16, Julio Di Egidio <julio@xxxxxxxxxxxxx> wrote:
So, let's restate it:

Within N* (that is, N U {oo}):
n = oo => [1/n, 1] = [0, 1]

With a common definitions of operations in N*, yes 1/oo = 0 and so
[1/n, 1] = [0, 1] when n = oo.


Within N:
n -> oo => [1/n, 1] = (0, 1] -> [0, 1]

Your choice of notation is strange.

Is the first clause "n -> oo" supposed to be a limit? Of what?

Is the "=>" intended to represent logical implication? It is
certainly not true that [1/n, 1] = (0,1].

Regarding the second arrow (which also appears to be used as a limit),
whether [0,1] is the limit or (0,1], or even whether a limit exists,
depends upon what sort of limit you are using - which you haven't
defined either.


- Tim
.

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