12:42 PM
Naturally, the two fact mentioned above are equivalent in the sense that one of them implies the other one.
Fact 1. If A≥B-ε is true for every ε>0 then A≥B.
Fact 2. If A≤B+ε is true for every ε>0 then A≤B.
It should be relatively easy to prove Fact 2 if we already know that Fact 1 is true and vice versa.
