Reductio ad absurdum is a logical argument that attempts to disprove a statement by showing that, if the argument is taken to its extremes, the result is absurd, or illogical. Reductio ad absurdum is also called argumentum ad absurdum and appeal to extremes. It is the original basis of the mathematical proof by contradiction.
Statement: There is a smallest positive real number. Contradiction: However, since any real number can be divided by two, and a number divided by two is smaller than the original number, there must be a real number smaller than any number. Conclusion: Therefore, there can be no smallest positive real number.
The process of taking an argument to its logical extremes was used before the Greek philosopher Socrates. Socrates and Aristotle formalized and taught this method.
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