Number Sets

There are many subsets of numbers that comprise the set of Real Numbers:

Natural Numbers ... are a subset of 

Whole Numbers
... which are a subset of 

... which are a subset of 

Rational Numbers
... {fractions and terminating decimal numbers in addition to the above numbers}
which are a subset of the Real Numbers.

Irrational numbers are not subsets of all of the above mentioned sets.  Irrational numbers are numbers that are non-terminating, non-repeating decimal numbers and are very different from Rational Numbers.
[ “ir” at the beginning of a word means “not”; thus, irrational means “not” rational.]

Most often Irrational numbers can be distinguished from other numbers by the use of the radical sign  .  However, if the radicand (the number inside the radical) is a perfect squared number, you could easily mistake the radical for an irrational number.  For example:  is a Natural number, a Whole number an Integer, a Rational number, and a Real number.    is a Rational number and a Real number.

  goes on and on forever with the decimals not repeating nor terminating.

Therefore, is an Irrational #.

Irrational numbers are a subset of the Real Numbers.  All numbers that we will be studying this semester are Real Numbers.  That means that all can be located on the number line.

General Algebra Tips

The views and opinions expressed in this page are strictly those of Mary Lou Baker.
The contents of this page have not been reviewed or approved by Columbia State Community College.

This page was edited on 09-Jan-2014