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The article says: 'A definition MUST be an "if and only if" statement.' It is an established convention in mathematics to write definitions in the form "X is Y

The article says: 'A definition MUST be an "if and only if" statement.' It is an established convention in mathematics to write definitions in the form "X is Y if P(X)". For example: "A metric space M is complete if every Caychy sequence in M converges in M". One may question whether this is a good convention, but it is a convention that most mathematicians tend to follow.

jordigh 9y ago
That's because the other direction is implicit. "X is a rectangle if it's a quadrilateral with all right angles." Okay, so you can use this statement to look at an object and then check if it's a quadrilateral with all right angles, and then conclude that, by definition, it's a rectangle. But for the other direction, if I tell you it's a rectangle, it's implicit that you can conclude all right angles. Contrapositively, it's also implicit that if I say it doesn't have all right angles, you can conclude that it's not a rectangle, i.e. that this condition has to be satisfied for anything worthy of the "rectangle" name. https://math.stackexchange.com/questions/566565/are-if-and-iff-interchangeable-in-definitions https://math.stackexchange.com/questions/566565/are-if-and-i...