Re: The set of necessary FISONs

On 30.01.2025 22:59, FromTheRafters wrote:

WM explained on 1/30/2025 :

On 30.01.2025 20:54, FromTheRafters wrote:

WM explained on 1/30/2025 :

On 30.01.2025 11:41, FromTheRafters wrote:

WM formulated the question :

On 29.01.2025 15:04, FromTheRafters wrote:

WM explained on 1/29/2025 :

On 29.01.2025 10:38, FromTheRafters wrote:
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Omega has no immediate predecessor.

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What is immediately before ω?

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Nothing, it is the initial member of the transfinite ordinals. just as zero is the initial member of the finite ordinals.

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There is something before zero.

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Not in the ordinals, which is what you say the context is this time.

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Not in the known ordinals. But if anything else, then name it, and how many of these are there.

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And how long is the distance from ω to a natnumber?

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This makes no sense.

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It is research.

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Is there a 'distance' metric in the ordinals?
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No, there is no inherent "distance" metric in ordinal numbers

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Wrong. The ordinals 7 and 27 have the distance 27 - 7 = 20.

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Finite ordinals are like finite cardinalities.

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Fine. Why do you mention this triviality?

 Because you treat ordinals as if they were cardinals.

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Cardinals are quantities and have no distances. Ordinals increase step by step on the ordinal axis. They describe distances from 0, and therefore have distances.