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## Main Question or Discussion Point

Why do membership chains ([tex]a\in b\in c\in ...[/tex]) have length at most [tex]\omega[/tex]?

- Thread starter Dragonfall
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- #1

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Why do membership chains ([tex]a\in b\in c\in ...[/tex]) have length at most [tex]\omega[/tex]?

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CRGreathouse

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Perhaps you mean [itex]a\ni b\ni c\ni\cdots[/itex], which has length less than [itex]\omega[/itex] by the axiom of regularity/foundation?

- #3

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All chains in [tex]\omega[/tex] are finite.

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