Talk:Passing to the infimum

Yes, and moreover:
If [ilmath]\forall a\in A\exists b\in B[b\le a][/ilmath], then every lower bound of [ilmath]B[/ilmath] is a lower bound of [ilmath]A[/ilmath]. Thus, [ilmath]\inf B[/ilmath] (if exists) is a lower bound of [ilmath]A[/ilmath]. Thus, if also [ilmath]\inf A[/ilmath] exists, then [ilmath]\inf B\le\inf A[/ilmath].
No need to assume that the two are comparable. Boris (talk) 08:02, 17 April 2016 (UTC)