Equivalence of Completeness Properties
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Feb16-12, 10:12 AM
Here's an approach you could try. Let a
be a bounded increasing sequence, which means that the sequence has an upper bound b. Then ([a
,b]) is a nested sequence of ntervals. Can you take it from here, using properties 1 and 2 to prove 3? And then you can do the analogous thing for bounded decreasing sequences.
If by property 1 you mean the least upper bound property the point here is not to use it!
I want a proof 2-3 without using 1,3,4,5