Let A be a subset of B. Then A is a proper subset of B if A is not equal to B itself. Thus there is some element of B not in A. The subset A is then said to be properly (or strictly) included in B, and this is written A ⊂ B. Some authors use A ⊂ B to mean A ⊆ B (see subset), but they then have no easy means of indicating proper inclusion.