Question

Suppose A is a subset of R (real numbers) sucks that both infA and supA exists....

Suppose A is a subset of R (real numbers) sucks that both infA and supA exists. Define -A={-a: a in A}.

Prive that:

A. inf(-A) and sup(-A) exist

B. inf(-A)= -supA and sup(-A)= -infA

NOTE:

supA=u defined by: (u is least upper bound of A) for all x in A, x <= u, AND if u' is an upper bound of A, then u <= u'

infA=v defined by: (v is greatest lower bound of A) for all y in A, v <= y, AND if v' is a lower bound of A, then v' <= v

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