Question: Let S be a non-empty subset of R. Define for a,b > 0, the set aS + b = {ax + b : x S}

Let S be a non-empty subset of R. Define for a,b > 0, the set aS + b = {ax + b : x S}

Prove that sup(aS + b) = a sup(S) + b and

inf(aS + b) = a inf(S) + b.

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