Is the following proof correct? if it isn't circle the first error you see and verify if it can be corrected to be proven true. Claim: If f: [a,b] → R is continuous and not constant, then its range is a closed, bounded interval. Proof: Since f is continuous on a compact domain, its range is compact and hence closed and bounded. Since the range is bounded, it has a supremum and an infimum. Since the range is also closed, the supremum and infimum belong to the range. Therefore the range is the closed and bounded interval [m,M], where m is the infimum and M is the supremum of the range.

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.