I’m currently learning it from scratch and I think that I pretty got the general idea: Supremum is largest limit of a set/sequence and infimum is the smallest.
I’ve encountered the following definition and found it difficult to fully understand the second statement:
$S$ is a supremum of a sequence/set $A$ if and only if: 1. $$x \le S , \forall x \in A$$ And 2. $$ \forall \epsilon > 0 , \exists X_0 \in A$$ So that $$X_0 > S- \epsilon$$
I managed to understand the definition of sequence and functions limits which involves epsilons and deltas also bust this one isn’t as clear to me as them, I’d be glad to get a better explanation. Thanks for helping :)