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just

One use of the word just in mathematical discourse is to indicate that what precedes satisfies the statement that occurs after the word “just”.

Example

(Assuming r and s are known to be integers greater than 1).

“... Then m = rs. But that is just the definition of ‘composite’.”

(Or “That just means that m is composite”.)

Remarks

In such sentences, “just” may commonly be omitted without changing the meaning, but in many cases it probably shouldn’t be omitted because it is an important indicator of the logical flow.

Before I did the research (finding citations of usage) for the Handbook, my own perception of this usage was that the word “just” meant that what followed was equivalent to what preceded. That’s a small example of the vital necessity of checking citations before making pronouncements about math English!

just in case

This phrase means that what follows is logically equivalent to what precedes. A search of Jstor reveals that in math research articles it is used mostly but not entirely by logicians.

Example

“An integer is even just in case it is divisible by 2.”

Remark

In ordinary English (used more in Britain than in the USA, I think), “just in case” means “to guard against the possibility of” (perhaps undesired possibility).

“I will take an umbrella just in case it rains”

means something like

“I will take an umbrella in order to guard against the (undesired) possibility that it might rain.”

This can cause cognitive dissonance: The statement “An integer is even just in case it is divisible by 2” certainly does not mean “An integer is even in order to guard against the possibility that it might be divisible by 2.”

Acknowledgments

Thanks to suggestions from Geoffrey K. Pullum. See his Language Log entry concerning this phrase.