Real Analysis Is the proof for this claim correct? State that it is correct, or circle the first error you see if it isn't, and explain 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.