Could anyone give me some idea's on where to go with this question?
The question ask's to use the definition of a supremum, which i know is:
2026-03-28 00:36:55.1774658215
using the definition of a supremum
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You are asked to show that $1$ is too small to be the supremum, but $2$ isn't.
In other words, show that $2$ is an upper bound of $E$ (not necessarily the least upper bound, which is the supremum), while $1$ is not.
The supremum fulfills two properties: in your definition one property relates to $\gamma + \epsilon$, and the other to $\gamma - \epsilon$. The former makes sure that $\gamma$ is large enough, and the latter makes sure that $\gamma$ is small enough. The latter is irrelevant in this specific problem.