Question

Show that sup{1 - 1/n | n in N} = 1

Answer 1

From intuition, it makes sense that 1 - 1/n only approaches 1 as n gets infinitely large. But that's not quite a proof.

I believe there are two steps to make this proof: (1) Show that 1 is an upper bound, and (2) Show that there is no upper bound smaller than 1 (i.e., 1 is least upper bound / supremum).
That is clear? Have you made any attempts so far from there?