contained in

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It is tempting to say that ‘x is contained in S’ when xεS, and also to say that ‘A is contained in B’ if AB. To distinguish between these two different notions, it is better to say that ‘x belongs to S’ and to say that ‘A is included in B’ or ‘A is a subset of B’. However, some authors consistently say ‘is contained in’ for⊆. Given the same examples, it is similarly tempting to say that ‘S contains x’ and also that ‘B contains A.’ It is again desirable to distinguish between the two by saying that ‘B includes A’ in the second case, though some authors consistently say ‘contains’ in this situation. The first case is best avoided or else clarified by saying that ‘S contains the element x’ or ‘S contains x as an element.’

Subjects: Mathematics.

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