Jech's Set Theory book says "if $C$ is a nonempty class of ordinals, then $\bigcap C = \inf C$". Why doesn't it just say "least element" instead of "infimum" ?
If $C$ is a nonempty class of ordinals, would $\bigcap C$ be the least element of $C$?
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set-theory
ordinals
1 Answers
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It could indeed say "least element". I suspect that Jech is using "inf" since it is more versatile - $\inf$ agrees with $\min$ wherever the latter is defined, but is defined for a broader class of linear orders. (Of course, one could equally well argue the other way - that "$\min$" should be used to emphasize the fact that the ordinals are well-ordered.)