Re: Replacement of Cardinality

Chris M. Thomasson used his keyboard to write :

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

On 8/13/2024 9:07 AM, FromTheRafters wrote:

WM used his keyboard to write :

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.

>
Right there where the negative axis begins?

 Ahh! Touche. :^D
 Well, lets say the real axis, or x axis if you will:
 (...)<--(-1)<--(-0+)-->(+1)-->(...)
 It's infinitely long... Notice the signed zero? lol. Fair enough?
 

>
I consider zero to be the origin for any n-ary axes system. For 2d (0, 0), 3d (0, 0, 0) for 4d (0, 0, 0, 0), 5d (0, 0, 0, 0, 0), ect, ect... ;^)

I prefer the unsigned version. Sometimes the set of naturals is called the positive integers and the naturals with zero as non-negative integers.