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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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Can you give an example? –  Rudy the Reindeer Dec 13 '12 at 11:19
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Absolutely not. All the definitions I can recall are either of the form "$X$ is $Y$" or "We say $X$ if $Y$". Even the first line of Euclid is declarative: Σημεῖόν ἐστιν, οὗ μέρος οὐθέν. –  Zhen Lin Dec 13 '12 at 11:24
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The examples you have cited are not really definitions; rather, they are hypotheses. –  Zhen Lin Dec 13 '12 at 11:40
    
@ZhenLin You are right, I will edit my question. –  Phira Dec 13 '12 at 12:06

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