Short summary of the essentials of set theory

[Fredrik]

I've been talking to a guy who doesn't know anything about sets, and I couldn't think of anything good to recommend that he should read. I know that there are lots of good books about set theory, but don't they all cover too many details so that it takes too long to get an overview of the basics? What I'd like to find is a good summary, no more than 20 pages long (5-10 pages would be better), that briefly explains the following, and doesn't bother to use the ZFC axioms to justify their validity:

The symbols $\forall,\exists,\in$. The two ways to specify a set. When are two sets equal? Unions, intersections, differences, complements, cartesian products. Functions (domain, codomain, range, pre-image, etc.). Ordered n-tuples.

I'm thinking that there must be a good book on analysis or topology or something that includes a summary that fits this description.

Oh yeah, it's preferable if the relevant pages are available online.

 

[jasonRF]

A short coverage that I found useful was in chapter 2 of "analysis with an introduction to proof" by Lay - I used the second edition since it was dirt cheap online. University library may have a copy of some edition of this book. I never took any theoretical math and it was just right for me - I suspect the guy you are talking to is in a similar boat. There are likely better options, but if no one else answers it is one that I know.

There are also quite a few free "proof" books online, but they tend to have longer coverage with lots of material in between sets and functions. But free is good! An example that looks good but I haven't read in detail:

http://www.people.vcu.edu/~rhammack/BookOfProof/

Hopefully others familiar with more books than I am will chime in...

jason

 

[Fredrik]

Thank you Jason. That looks very good. The number of pages is higher than I wanted, and somehow the { and } symbols are messed up so that only the upper half of them is displayed (I'm assuming that wasn't on purpose), but the content looks very solid and very readable.

 

[mathwonk]

I didn't see anything on the most important topic you mentioned, namely functions, in those notes.

Kahn academy has a good rep, so here is their video lineup, but i have not watched them.

http://www.khanacademy.org/math/trigonometry/functions_and_graphsOf course you realize your page limit was ludicrously short, but the first 35 pages of Halmos' classic book Naive Set Theory, comes close:

https://www.amazon.com/dp/1614271313/?tag=pfamazon01-20

 

[Fredrik]

Thank you mathwonk. Those tips look interesting. I realize that I was a bit optimistic about how short one can make a quick intro, but this pdf shows that I wasn't completely crazy. It covers most of the things I mentioned in only ten pages.

http://people.umass.edu/partee/NZ_2006/Set Theory Basics.pdf