=See the section in this article about that topic. http://en.wikipedia.org/wiki/Set_(mathematics)
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There are two ways of describing, or specifying the members of, a set. One way is by intensional definition, using a rule or semantic description: The second way is by extension - that is, listing each member of the set. An extensional definition is denoted by enclosing the list of members in curly brackets:
You can make 125 different 3-digit numbers if you're allowed to repeat a digit (for example, 113, or 545), and 60 if you're not. If repetitions are allowed, then there are 5 ways to choose each digit to be 1,2,3,4, or 5, so the total number of ways is 5*5*5 or 125. If no repetitions are allowed, there are 5 ways to choose the first digit, but only 4 ways left to choose the second (for a total of 5*4=20 ways to choose the first two digits), because it can't be the same as the first. Then you have eliminated two choices for the third digit, so there are only 3 ways to choose it, for a total of 5*4*3=60 different 3-digit numbers.
The empty set is a subset of all sets. No other sets have this property.
The set of all real numbers (R) is the set of all rational and irrational numbers. The set R has no restrictions in its domain and so includes (-∞, ∞).
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