And I do mean superficial; all you will learn here is a few definitions, what the set-theoretic symbols mean, and some very basic concepts.

So, asetis simply a collection of objects for which I can find a suitable unifying property which will allow me to make the following assertion:

A set is well-defined iff, for any object whatever in the universe of objects, an object is either in the definitely in this set or definitely not in this set.

We will see that this assertion neatly side-steps a famous paradox.

Obviously, the objects we shall be dealing with here aremathematicalobjects. Let's now look at the "algebra" of sets (it's not, of course, really an algebra!), so we will need some notation.

One says that S is a set, and that if one wants to assert that "x is a member of (an element in) S". In like fashion, it is sometimes syntactically convenient to write to mean "S is the set that has x as a member".

(Caveat: militant set theorists will insist these two forms are subtly different - let them go hang!).

Conversely, one would write to mean that x is not an element in S.

More notation: when talking about a set, one has two choices; one can give the entire set a label, like X or Y or whatever, or one might want to be more specific. Write, say, X = {x, y, z} to mean that "X is the set whose elements are x, y and z".

Note that this formulation isvery rarely usefulwhen x, y and z are not fully defined. The exceptions include, say, Y = {2, 4, 6, 8, 10, ...}, where one may may assume that Y is the set of even numbers.

This brings us full circle for now, and to some useful notation which, unexpectedly, reveals something slightly profound. Recall we agreed that a set is a collection which has a strict membership criterion. In other words, a set is really a collectiontogether withthat criterion. We write it like this:

X = {x : membership criterion}. Here's a concrete example. 3Z = {x : x is integer exactly divisible by 3}. Read the colon ( the pipe | is also used) to mean "such that", or "with the property that".

Here is the slight profundity; sets are pretty dumb creature, as we shall see - they know nothing about, say, division (as in the example above). But we are not dumb - we can establish the qualification for set membership in any way we choose, but once "inside the set" the members are not allowed (in general) to use that qualification.

Like, throw a party for footballers only, but stipulate that no football is allowed inside your house.

You'll be tired of reading this drivel, no doubt, and I have barely scratched the surface.

Later, but ask questions, make corrections, put me on ignore, whatever.....