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 

Integers ... 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.