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I'm thinking that since it's bounded below by 0 and the set contains it's bound that if I can show that it's closed and bounded above that will be a proof but i'm not really sure how i would do that

or

Say there's an collection of open sets who's union is (-2, 2^-m + 2^-n + 2) that since that's an open cover then and you can have a finite subcover of something like (-1, 2^-m + 2^-n +1) that'll still contain the set therefore the set is compact.

I don't know if either of those are correct or if i'm heading in the right direction. Can anyone help?