In a mathematical proof (using the induction), when I deal with the base case, which is (if any) correct?

  1. The case when n=1 is trivial
  2. The case n=1 is trivial

I would like to know if I need "when" or not.

2 Answers 2


Since it's unlikely that you're trying to prove n=1, "the case when n=1" is more likely to be appropriate.

Both are correct, but mean slightly different things. "The case n=1" means just that n=1, "the case when n=1" is referring to a broader equation or concept with n, and n is 1. For instance, you are trying to prove that the sum of the sum of the first n odd numbers is n^2 and your base case is n=1.

Source: native speaker of English, studied college-level math

  • I am not sure what you mean by a broader equation. Could you give me examples that illustrate the difference?
    – Eng
    Dec 31, 2016 at 6:22

Since n=1 is a special case, it doesn't really need the 'when'. Adding the 'when' would be appropriate if you're jumping forwards, e.g. "the case when n=55 is interesting because..."

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