## Proof Exercise #3 Continuation 2:

proving the Heine-Borel Covering Theorem

Yes.

Notice completing the proof can be done by showing that b is such an x. Taking this approach, we what to "push" such an x towards b as far as possible. What, from the list below, will be our approach for doing so?

choice #1: Consider the set of all such x.

choice #2: Consider the Pythagorean Theorem.

choice #3: Consider the distance from a to b.

choice #4: Consider the absolute values of a and b.

choice #5: Consider the rational numbers in [a,b].

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Notice completing the proof can be done by showing that b is such an x. Taking this approach, we what to "push" such an x towards b as far as possible. What, from the list below, will be our approach for doing so?

choice #1: Consider the set of all such x.

choice #2: Consider the Pythagorean Theorem.

choice #3: Consider the distance from a to b.

choice #4: Consider the absolute values of a and b.

choice #5: Consider the rational numbers in [a,b].

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