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Let [itex]A\subset \mathbb R[/itex], and let [itex]|A| = \{|a|:a\in A\}[/itex]. Then [itex]\sup |A| = \max \{|\inf A|, |\sup A|\}[/itex].

I think I could figure this out on my own, but there is something else demanding my attention right now...so, hopefully this isn't too tough. Thanks!