Re: Replacement of Cardinality

On 8/13/2024 12:10 PM, Chris M. Thomasson wrote:

On 8/13/2024 7:17 AM, WM wrote:

Le 12/08/2024 à 19:23, Richard Damon a écrit :

On 8/12/24 9:50 AM, WM wrote:

>

What causes an exception: nₓ ∈ ℕ:
⅟nₓ > 0 without ⅟(nₓ+1) > 0 ?

>
The end of the positive axis.

>
Which, by the definition of the Natural Numbers, doesn't exist.

>
The end of the positive axis exists.

 Nope. Just like there is no end to the negative x axis. Oh, there is no end to the y axis as well. The z axis, the w axis, on and on wrt n-ary axes... :^)
 

Well, let me add a correction:
(...)<--(-1)<--(-0+)-->(+1)-->(...)
So, there is an "end" wrt the transition from positive to negative at zero. Sorry about that.