# Quick set builder notation question

1. Feb 12, 2005

### EProph

I've seen a lot of variety in the way different books/people use set builder notation. Is their any "standard"?

For example, I've seen:
{x | x < -2 or x > 2 }
And somtimes:
{x | x < -2 U x > 2 }
And also:
{x | x < -2 } U {x | x > 2}

Is any one of these more "correct" than the others?
Thanks,
-EP

2. Feb 12, 2005

### dextercioby

There's a clear difference between the first & the second...I don't like the third,i've neve seen it b4.

Daniel.

3. Feb 12, 2005

### mathman

The first and third expressions are equivalent. The word "or" is a logic term, while the "U" is the set theoretic analog. The second expression doesn't look right to me. I believe it should have a "V", which is the logic symbol for "or".

4. Feb 13, 2005

### mathman

There is a slight technical difference between the first and third expression, although they are equivalent. In the first expression the set in question is defined directly. In the third expression, it is the union of two smaller sets.

5. Feb 13, 2005

### EProph

Thanks, this makes sense. I see the diffence now. 1 and 3 both result in the same set, but they build it in different ways.

-EP

6. Feb 13, 2005

### Zurtex

Actually it depends how you define the word or, when said out loud it can mean what we use mathematically as XOR, so I would tend towards using the 3rd.

7. Feb 13, 2005

### mathwonk

it is absic principle that the set of elements such that either A or B is true, is the union of the set such that A is true, with thes et such that B is true.
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So the first and third expressions are both standard and necessary, and it is a trivial theorem, that they are the same set.

but the symbol V for or is a logical symbol, whiler the symbol U is a set theoretic symbol, hence are used in different contexts, and probably no one would advocate discarding one in favor of the other. they are both useful.