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Show that if S and T are non-empty and bounded above, then sup(S∪T) = max(supS,supT)

Any ideas on how I would approach a proof for this?

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closed as off-topic by Jyrki Lahtonen, Calvin Khor, Xander Henderson, Don Thousand, José Carlos Santos Nov 9 at 15:41

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    $\begingroup$ I'd start by recalling the definitions of sup and max, and very legalistically figuring out what I need to show, given what the assumptions tell me, $\endgroup$ – kimchi lover Nov 8 at 15:09

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