Re: because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/13/2024 1:27 PM, WM wrote:

Le 10/05/2024 à 20:56, Jim Burns a écrit :

On 5/10/2024 8:18 AM, WM wrote:

Le 08/05/2024 à 23:55, Jim Burns a écrit :

On 5/8/2024 3:55 PM, WM wrote:

Le 07/05/2024 à 00:11, Jim Burns a écrit :

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All which canNOT be counted.to are not.in ℕ

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All which canNOT be counted.to are not.in ℕ_def.

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And all which CAN be counted.to are in ℕ_def.

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Yes.

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Thank you.
>
ℕ_def is the set of all and only
numbers which CAN be counted.to.
ℕ_def is what everyone else calls ℕ

 Yes, most are too stupid to see the difference: ℕ contains numbers which never can be counted to.

Think of a little kid that knows 1, 2, 3, 4, 5, however the kid does not know about 6 or 42, or 128, or 103. According to you, those numbers do not exist? Or, kind of dark as you say?
ℕ shades of gray?
Wow.

 

ℕ_def is a potentially infinite collection
and as such has no fxed number of elements.
We use the indefinite oo in this case.

>
Weⁿᵒᵗᐧᵂᴹ use ℵ₀ to refer to |ℕ_def|

 ℕ_def contains only numbers which can be counted to and which have ℵ₀ successors. f |ℕ_def| = ℵ₀ would  be succeeded by ℵ₀.
 Regards, WM