Re: Incompleteness of Cantor's enumeration of the rational numbers (extra-ordinary)

Am 09.01.2025 um 23:49 schrieb Chris M. Thomasson:

On 1/9/2025 2:12 PM, WM wrote:

On 09.01.2025 21:46, FromTheRafters wrote:

WM has brought this to us :

>

No, I simply know that all natural numbers exist and then comes ω.

Right.

No, after the natural numbers comes omega plus one. Omega *IS* the order type of the natural numbers.

<facepalm>
Hint: 0 < 1 < 2 < 3 < ... < ω < ω+1 < ω+2 < ω+3 < ...

ω is the first infinite ordinal number. It comes after all finite ordinal numbers and can be considered as their limit. The order type is another meaning of ω.

Right.

Nothing from that implies that there is a "largest natural number". Not at all. :^)

Indeed.
But when thinking of (or trying to imaging) that ... part here:
             0 < 1 < 2 < 3 < ...
WM's brain explodes.
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.
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