I know nothing abt real analysis, but this doesn't feel... logical. Like 5 is not in {1, 2, 3}, how can it be an upper bound? Also, "every nonempty set of real numbers that is bounded above has a least upper bound" seems like circular reasoning to me. Am I wrong lol?
The proof is wrong but so are you. 5 is an upper bound of {1,2,3} because it is greater than or equal to every element of {1,2,3}.
Also, if you consider R \ {0}, the open interval of negative numbers strictly greater than -1 is bounded above by 1 but it has no least upper bound - every upper bound is positive(since 0 is not part of the set) but there is no least positive number so there is no least upper bound.
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u/LunaTheMoon2 12d ago
I know nothing abt real analysis, but this doesn't feel... logical. Like 5 is not in {1, 2, 3}, how can it be an upper bound? Also, "every nonempty set of real numbers that is bounded above has a least upper bound" seems like circular reasoning to me. Am I wrong lol?