Let's talk about the various subsets
of real numbers.
One subset is
counting
(or natural) numbers. This subset includes all the numbers we
count with starting with "1" to infinity. The subset would
look like this:
{1, 2, 3, 4, 5...} 
Another subset is
whole
numbers. This subset is exactly like the subset of counting
numbers, with the addition of one extra number. This extra
number is "0". The subset would look like this:
{0, 1, 2, 3, 4...} 
A third subset is
integers. This subset includes all the whole numbers and their
opposites. The subset would look like this:
{... 4, 3, 2, 1, 0, 1, 2, 3,
4...} 
Notice that so far none of these
subsets have included decimal numbers or fractions. The next two
subsets include decimal numbers and fractions.
The next subset is
rational numbers. This subset includes all numbers that "come
to an end" or numbers that repeat and have a pattern. Examples
of rational numbers are:
5.34, 0.131313..., 6/7, 2/3, 9 
Lastly we have
irrational numbers. This subset includes numbers that cannot
be exactly written as a decimal or fraction. Irrational
numbers cannot be expressed as a ratio of two integers.
Examples of irrational numbers are:
,
,
and
π 
Ready to
practice?
