Can the statements be used interchangeably?

(1) The set-builder notationdefinesa set.

(2) The set-builder notationdescribesa set.

I'm really confused with these two words.

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- Jun 2nd 2010, 06:03 PMmamenDefines/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. - Jun 2nd 2010, 09:00 PMundefined
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}.