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## Homework Statement

Let a(n) and b(n), n[tex]\in[/tex]N, be some real numbers with absolute value at most 1000. Let A={a(n), n[tex]\in[/tex]N}, B={b(n), n[tex]\in[/tex]N}, C={a(n) + b(n), n[tex]\in[/tex]N}. Show that

inf A + sup B [tex]\leq[/tex] sup C [tex]\leq[/tex] sup A + sup B

## The Attempt at a Solution

I was thinking that I could show that inf A + sup B = 0, and that sup C is larger than 0, and then that sup C = sup A + sup B. The only problem is that I am terrible at writing formal proofs, and could really use some help with the language, and (probably) my logic.