2.3 Bounds of sets of real numbers - Ohio State University
0 < B 0 then a < B. Otherwise a 0 = B 0 and we go on to compare the first decimals. Either a 1 < B 1 therefore a < B or, otherwise, a 1 = B 1. Etc. So either a < B or a = B. So B is an upper bound. To show it is the least (upper bound), take any smaller number t < B. Then t differs from B at some first decimal, say at the nth decimal: t = B ...
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