Re: The set of necessary FISONs

On 31.01.2025 16:47, FromTheRafters wrote:

WM has brought this to us :

On 31.01.2025 14:12, FromTheRafters wrote:

WM formulated on Friday :

On 31.01.2025 11:43, FromTheRafters wrote:

WM explained :

On 31.01.2025 11:02, FromTheRafters wrote:
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Ordinals aren't guaranteed to increase.

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What ordinal has not a greater successor?
Ordinals n are well-ordered. The distance from 0 is n - 0 = n.

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Starting with omega, they are all countably infinite until you reach the uncountably infinite.

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ω < ω + 1, < ω + 2 < ... < ω + ω = ω2 < ω2 + 1 < ...

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Each of which is countably infinite.

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That is not of interest. According to Cantor, every set of ordinals has a smallest element. Each is greater than its predecessor.

 What is meant by 'greater' in this context?

The contrary of smaller. "Theorem B: Every embodiment of different numbers of the first and the second number class has a smallest number, a minimum." [Cantor, p. 332]
Regards, WM