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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 7

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Implications

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Mathematics consists of propositions of the form: P implies Q, but you never ask whether P is true.

Bertrand Russell

Russell’s quote above is extremely incisive. Modern mathematics is indeed made up of statements of the form statement P implies statement Q. That is, we have ‘If statement P is true, then statement Q is true also.’ Usually, however, this structure is hidden, mainly to make mathematics more comprehensible – it would be hard to read if we always wrote it that way.

The second part of Russell’s quote is also true ...

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