2
$\begingroup$

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 ...

  • 0
    Can you give an example?2012-12-13
  • 2
    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.2012-12-13
  • 3
    The examples you have cited are not really definitions; rather, they are _hypotheses_.2012-12-13
  • 0
    @ZhenLin You are right, I will edit my question.2012-12-13

0 Answers 0