Re: Set Theory question

Stephen J. Herschkorn wrote:
thoughtcube@xxxxxxxxx wrote:

Let (A, <=) be an ordered (i.e. totally ordered) set. Then there exists
a series a_n of elements of A, for which: for any element a in A, there
is some a_n that is larger than it, i.e. a <= a_n.

The claim is false. No such series exists in omega-1.

Right. But interestingly, if choice fails it's possible that every
cardinal has cofinality omega.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus

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