(7.3.25) Does f∘h = g∘h with h Injective Always Imply f = g for Functions?
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(7.3.25) Does f∘h = g∘h with h Injective Always Imply f = g for Functions?
I analyze whether "if h is one-to-one and f∘h = g∘h, then f = g" holds for all functions. Initially, I believed this was true after testing multiple examples. I spent significant time attempting direct proofs and proofs by contrapositive without success. I eventually discovered the statement is false through a counterexample. I consider ...
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