Question: 2. Show that if E is a nonempty bounded subset of Z, then both sup E and inf E exist and belong to E. ~.

2. Show that if E is a nonempty bounded subset of Z, then both sup E and inf E exist and belong to E.

~. [DENSITY OF IRRATIONALS] This exercise is used in Section 3.3.

Prove that if a < b are real numbers, then there is an irrational ~ E R such that a < ~ < b.

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