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**Jhevon** a valid argument is one in which the conclusion follows logically from the premises and the conclusion is true (or very likely to be true) if all the premises are true. a sound argument is a valid argument that has true premises, and therefore, the conclusions that follow logically must be true (or must be highly likely to be true).

there is nothing wrong with the proof itself, it is a valid proof. however, it is not sound, since the premise is not true (there is no largest integer). therefore, we can assume that the conclusion is false, since, even though it follows logically from what we originally assumed, what we originally assumed was false.

you should also realize, an implication is only false, if we have a true statement implying a false statement, otherwise the implication is true. a false statement implies whatever, literally. the statement "if n is the largest integer then pigs can fly" is true as far as the truth table definition of an implication is concerned.

therefore, the only thing wrong with this proof is that its premises are false, and therefore any conclusion from it, even though that conclusion may be derived logically, is highly likely to be false--which in this case, we can clearly see that it is.