In set theory and other branches of mathematics, theunionof a collection of sets is the set that contains everything that belongs to any of the sets, but nothing else. IfAandBare sets, then the union ofAandBis the set that contains all elements ofAand all elements ofB, but no other elements. The union ofAandBis usually written "A∪B".

That's not what I though union would be, intuitively. What I thought would be the union, is the intersection:

In mathematics, theintersectionof two setsAandBis the set that contains all elements ofAthat also belong toB(or equivalently, all elements ofBthat also belong toA), but no other elements. The intersection ofAandBis written "A∩B".

Also interesting is symmetric difference:

symmetric differenceof two sets is the set of elements which are in one of the sets, but not in both. This operation is the set-theoretic equivalent of the exclusive disjunction (XOR operation) in Boolean logic. The symmetric difference of the setsAandBis commonly denoted byThe symmetric difference is equivalent to the union of both relative complements, that is:

## 4 comments:

I love set theory.

ndjke

I was seriously just about to post, "I love this shit."

How weird is that?

I've only dabbled my toes in the set theory waters, but I think I like.

Something our Algebra teacher said was interesting. He mentioned that when he went to K-12, they didn't talk about sets. He's probably in his 50's. I wonder if that was a general curriculum thing?

I'm not 100% sure we did sets in high school, it might have been college. I have a hard time now figuring out what went where in my education from 2nd grade to now. I only have K-2nd figured out because Margot's in 2nd grade now.

kfqyoi

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