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In mathematical hypotheses it is traditional to use the imperative instead of a declarative sentence.

What is the origin of this tradition? Does it go back to ancient Greek mathematics? Or maybe to Bourbaki?

This is clearly a usage that exists in different languages:

Let $n$ be an integer ...
Soit $n$ un entier ...
Sei $n$ eine ganze Zahl ...

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    @ZhenLin You are right, I will edit my question.2012-12-13

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