The Completeness axiom and a proof by contradiction

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We explain the statement of the completeness axiom, and determine the supremum of a set using a proof by contradiction.
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I don't understand how you come up with n less than or equal to 1 over enlighten me. Can you do it step by step?

bntv
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3:47 do we need to sayN* to terminate 0 but 0 itself doesn't lie in N

hiteshattri
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I have questions. At what expense do I play said lotteries? How many other players are there and how many tickets are they buying? What if I can't answer because I feel indifferent about the prize? Why is this so vague? I need more data. Also, what's the deal with the definition of 'independence' in decision-making? Only because I'm sure that 'independence' should mean that I can choose whichever I like and it not be "right" or "wrong" - excuse my confusion.

kjudge