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

Am 30.04.2024 um 15:12 schrieb WM:

{1, 2, 3, ..., ω}*2

= ({1, 2, 3, ...} u {ω})*2
= {1, 2, 3, ...}*2 u {ω}*2
= {2, 4, 6, ...} u {ω*2} (where {2, 4, 6, ...} = G c IN)

results in {2, 4, 6, ..., ω*2}

Exactly.
Then it's clear that

ω or ω+1 is [NOT] amidst [...]

Hint: ω !e {2, 4, 6, ..., ω*2} and ω+1 !e {2, 4, 6, ..., ω*2}.
Actually, the only infinite ordinal in {2, 4, 6, ..., ω*2} is ω*2.