Consider a sentence like

If $x \in \mathcal A$, then we define $f(x) = 0$.

Is it legetimate to replace "If" in that statement by "when", say, for the purpose of linguistic varietiy, such as in

When $x \in \mathcal A$, then we define $f(x) = 0$.

or is that considered bad style?

  • 3
    $\begingroup$ If and when have no real semantic difference. In German they're pretty much the same word "wenn". $\endgroup$
    – Jam
    Sep 5, 2016 at 13:58
  • $\begingroup$ There's nothing mathematically wrong with "when...then," but I don't think it's considered good English. Maybe "When $x \in \mathcal A$, define $f(x) = 0$" is better. $\endgroup$
    – D_S
    Sep 5, 2016 at 14:01
  • $\begingroup$ It is not "bad style" per se. Most mathematical Readers will immediately recognize "when" is being used to introduce a logical, rather than temporal, condition. If the discussion were about (say) a time-dependent solution of a PDE, then confusion is possible but not apparently in the circumstance you describe. The word "then" has its own temporal connotations in English ("That was then..."). $\endgroup$
    – hardmath
    Sep 5, 2016 at 14:03

1 Answer 1


"If/then" is a common English construct, but "When/then" is not. When one uses "when," they shouldn't start the next clause with "then." (c.f. "If one uses "when," then they shouldn't start the next clause with "then.")

In most cases, the two formations ("if x then y" and "when x, y") are equivalent.


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