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Warrigal comments on Logical Pinpointing - Less Wrong
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I'd say that your "non-well-defined function on fractions" isn't actually a function on fractions at all; it's a function on fractional expressions that fails to define a function on fractions.
Fair enough. We could have "number expressions" which denote the same number, like "ssss0", "4", "2+2", "2*2". Then the question of well-definedness is whether our method of computing addition gives the same result for each of these different number expressions.