View source for Talk:Passing to the infimum

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