1) "Least upper bound axiom:(adsbygoogle = window.adsbygoogle || []).push({});

Every non-empty set of real numbers that has an upper bound, has a least upper bound."

Why does it have to be non-empty? Is there an upper bound for the empty set?

2) "It can be proved by induction that: every natural number "a" is of the form 2b or 2b+1 for some b in N U{0}. "

The base case is clearly true, but how can we go from the induction hypothesis to the case for k+1?

Thanks for any help!

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# Least upper bound axiom

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