# Use of singular or plural in mathematics

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?

• I'm voting to close this question as off-topic because this question is more suited to mathematics.SE. Apr 12, 2018 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. Apr 12, 2018 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, 2018 at 20:51