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Math Help - Defines/describes

  1. #1
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    Post Defines/describes

    Can the statements be used interchangeably?

    (1) The set-builder notation defines a set.


    (2) The set-builder notation describes a set.


    I'm really confused with these two words.
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  2. #2
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    Quote Originally Posted by mamen View Post
    Can the statements be used interchangeably?

    (1) The set-builder notation defines a set.


    (2) The set-builder notation describes a set.


    I'm really confused with these two words.
    My understanding of the terminology is that (1) and (2) are both true, but (1) is stricter.

    So, whenever we define a set, we also describe it. But whenever we describe a set, we don't necessarily define it.

    So here's an example of a set description that is not a definition: A is a set with three elements.

    Here is a definition of a set, which is also a description: Let A = {1,2,3}.
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