I disapprove of ``glb'' and ``lub'' for inf and sup; these are
obviously training wheels, and they don't help me!

Here's a good mneumonic:
sUP is -up-: it's the max, kinda
mIN is INf, kinda

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I'm also a big fan of lim inf and lim sup:
they help you understand sequences better, and allow you to define
oscillation for functions

(and there's a nice picture: the band that a function/sequence stays
within)

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BTW, these are really trivial and easy concepts;
$(0,1)$ has no min or max, but has inf and sup;
there's nothing more to understand.

In any case, they originally gained prominence in a much juicier
context: Weierstrass raised the objection that
"you don't know that the inf of a variational problem will be -achieved-"
(or perhaps won't be achieved by a smooth function)
...which shows the importance of inf in a rather sophisticated and
-relevant- setting.

sups and infs are mostly actually used to hone students' proof skills.
