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kingwinner
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1) "Least upper bound axiom:
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!
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!