In mathematics we often need to refer to lists of numbers in the form of a_1, a_2, etc. which we denote in totality by a_n where n stands for 1,2,3,etc. Nevertheless it is not then clear whether a_n is a singular or a plural because in one sense a_n is an individual number (if n is taken to refer to a single number). So different authors use different versions, for example:

  1. Let a_n be a number such that ...; If a_n has the property...
  2. Let a_n be numbers such that ...; If a_n have the property...

My impression is that the majority of mathematicians use the first version. Which one is correct?

  • 2
    I'm voting to close this question as off-topic because this question is more suited to mathematics.SE. – AndyT Apr 12 '18 at 8:58
  • How can a list of numbers be a number? The clearest way of writing this seems to be that shown at Chegg Study: 'Suppose a sequence {a_n} has the property that for every ...'. This might be deleted to your version (1), but I wouldn't recommend doing so. – Edwin Ashworth Apr 12 '18 at 9:00
  • I guess it depends on what n is. If you say for all n in N then it's similar to for every element in N. If, however, n represents multiple numbers, then I'd use the plural. This might be the case when you say: for all 1<n<100, which is similar to saying: for all even numbers. – JJJ Apr 13 '18 at 20:51

"Which one is correct" depends on whether the writer intends to refer to an individual number or a set of numbers; there is no grammatical point beyond that. Of course, in most theorems it makes no difference which is meant, so you can choose either form so long as you remain consistent.

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