Yudhister Kumar

• Yudhister KumarOct 18, 2023, 2:17 PM

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  in reply to: quiet_NaN’s comment on: Hyper­re­als in a Nutshell

  I’m familiar with \setminus being used to denote set complements, so \not\in seemed more appropriate to me ($I$ is not an element of $U$). I interpret $I\setminus U$ as “the elements of $I$ not in $U$,” which is the empty set in this case? (also the elements of $U$ are sets of naturals while the elements of $I$ are naturals, so it’s unclear to me how much this makes sense)

• Yudhister KumarOct 18, 2023, 2:04 PM

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  in reply to: JBlack’s comment on: Hyper­re­als in a Nutshell

  The post is wrong in saying that U contains only cofinite sets. It obviously must contain plenty of sets that are neither finite nor cofinite, because the complements of those sets are also neither finite nor cofinite. Possibly the author intended to type “contains all cofinite sets” instead.

  Yep, this is correct! I’ve updated the post to reflect this.

  E.g. if an ultrafilter contains the set of all even naturals, it won’t contain the set of all odd naturals, neither of which are finite or cofinite.

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• Yudhister KumarMay 4, 2023, 2:43 AM

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  in reply to: gjm’s comment on: five ways to say “Al­most Always” and ac­tu­ally mean it

  Thanks for the advice! Still learning how to phrase things correctly & effectively.

  I wasn’t aware that you can’t actually explicitly construct a nonprincipal ultrafilter—this is interesting and nonintuitive to me!

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