Re: how

WM schrieb:

Le 11/04/2024 à 19:36, Jim Burns a écrit :

On 4/11/2024 8:07 AM, WM wrote:

 

Which ones were unused by e = 2*n?

>
Those of {1, 2, 3, ...} with less than ℵo successors.

 
{1,2,3,…} is
the least.upper.bound of all finiteⁿᵒᵗᐧᵂᴹ.{1,2,3,…,k}

 
Yes, but many natnumbers will never be used.
 

For each m ∈ {1,2,3,…}:
( for each k ∈ {1,2,3,…}
m+k is a successor of m in {1,2,3,…} )

 
Consider the set {1, 2, 3, ..., ω} and multiply every element by 2 with
the result {2, 4, 6, ..., ω*2}. What elements fall between ω and ω*2?

{w+1, w+2, w+3, ...,}

What size has the interval between N*2 and ω*2?

N*2 is not a number, so there is no interval between it and w*2