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Recall that (a,b)?R means an open interval on the real number line: (a,b)={x?R|a<x<b}. Let ? be the usual...

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Advance Math

Recall that (a,b)?R means an open interval on the real numberline:

(a,b)={x?R|a

Let ? be the usual “less than or equal to” total order on theset

A=(?2,0)?(0,2)

Consider the subset

B={?1/n | n?N, n?1}?A.

Determine an upper bound for B in A. Then formally prove that Bhas no least upper bound in A by arguing that everyelement of A fails the criteria in the definition of least upperbound.

Note:

least upper bound is an upper bound for B?A that is less thanevery other upper bound

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