Sets

This is of a bit vague. Some questions arise:

1. What kinds of things are we going to have as elements? Usually our sets will be sets of numbers of some kind, but they might also be sets of symbols or sets of sets.
2. What does ``well-defined'' mean? We want there to be a yes or no answer to the question of membership. Thus we can define a set of real numbers strictly between 0 and 1 (since for any real number we know what it means to be strictly within these bounds) but we don't have a set of ``really big'' numbers.
3. How can we specify sets? Some sets are so important we give them names (for kinds of numbers, look at the next section). We can also list elements explicitly (easiest if we are talking about a set of symbols) for example

   

   or give a rule for picking out members of some larger set:

   

It is useful to know ways to compare two sets:

This means that A=B means both and .