Recall that (a,b)?R means an open interval on the real numberline:
(a,b)={x?R|aLet ? 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
