No falsehoods in proofs!

In a mathematical proof we do not touch falsehoods at any point (see Note below for a minor exception). Any time a falsehood enters we are off the straight-and-narrow. In following clues, even when we are successful, the final product may not correspond exactly to the original.

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Note: In a reductio ad absurdum proof we assume the opposite of the proposition to be proved. By showing that this assumption leads to a contradiction and therefore false, we conclude that the proposition to be proved must be true. In the case of the reductio then, we do touch a falsehood but only as an assumption. Moreover, the point of the reductio is to show how dangerous it is if we have any truckings with falsehoods: they lead to contradictions!