Learn English – “elements in” vs “elements of”

grammaticalitymathematics

Let A be a set, which of the following is grammatically correct

  1. an element in A, elements in A, a subset in A, subsets in A, or
  2. an element of A, elements of A, a subset of A, subsets of A?

I have seen both used in the literature, but I am not sure if they are used correctly. If both are grammatically correct, is there any difference in the meaning?

Best Answer

When the context is about mathematical sets, the term elements of A is commonly accepted.

Two sets A and B are said to be disjoint, if no element of A is in B and no element of B is in A.

However, for other types of sets elements in A is also acceptable.

When you are referring to the number of elements, you say: the number of elements in A:

The number of elements in set A is 6.

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