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- There are serious and subtle difficulties in dealing with sets, so we will skirt round these.
**Examples**- The
**natural numbers N**= {1, 2, 3, ... }

- The
**integers Z**= { ..., -2, -1, 0, 1, 2, ... }

- The
**rational numbers Q**= {^{a}/_{b}∈**R**|*a*,*b*∈**Z**,*b*≠ 0} - All these sets lie inside the set of
**real numbers R**which is what this course is about. We will examine this in more detail later. **Some notation**

If*A*,*B*are sets then*A*∪*B*and*A*∩*B*are the usual*union*and*intersection*.

*A*×*B*(the*Cartesian product*) is the set of all ordered pairs: { (*a*,*b*) |*a*∈*A*,*b*∈*B*}.- When we talk about the Real number line
**R**, we use the following notation for intervals.

An**open interval**: (*a*,*b*) = {*x*∈**R**|*a*<*x*<*b*} does*not*contain its end points.

A**closed interval**: [*a*,*b*] = {*x*∈**R**|*a*≤*x*≤*b*} does contain its end points.Some other intervals: [

*a*,*b*), (*a*,*b*], (-∞,*b*], (*a*, ∞), etc.

(See Some Early History of Set Theory.)

For the moment, think of a **set** as a *collection of elements*.

We will assume familiarity with some of the following examples.

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