Various Subsets of Real Numbers - Lesson
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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?

 

 

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