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## Subsets of Real Numbers

Subsets of Real Numbers

Natural Numbers -are used for counting and the set does not include zero.

$1, 2, 3, 4, 5, ...$

Whole Numbers – include the set of natural numbers and zero.

$0, 1, 2, 3, 4, 5, ...$

Integers – includesÂ  zero, the set of natural numbers, commonly called the positive integers and the opposite of the natural numbers.

$... -2, -1, 0, 1, 2 ...$

Rational Numbers – include any number that can be represented by the quotient of two integers. In that quotient the denominator must not be zero.

Given that a and b are integers, then $\frac{a}{b}$ where $b \neq 0$.

There are all kinds of numbers that fit this description. Any combination of the fractions with the subsets above fit the definition of a rational number.

It is good to remember that all numbers that are termination decimals such as $0.25 =\frac{25}{100}= \frac{1}{4}$ and $0.4 =\frac{4}{10}= \frac{2}{5}$.

Let’s not for get those decimals that have a pattern that can be identified as repeating. Here are just two examples: $0.\overline{6} = \frac{2}{3}$ and $0.\overline{4} = \frac{4}{9}$.

Irrational Numbers$\pi$, $\sqrt{2}$, $\sqrt{5}$, $\sqrt{\frac{6}{7}}$, $1.021502160217...$

These are just a few of the examples of irrational numbers. If a number does not fit in as one of the other numbers, it is irrational. There is another set of numbers to, but that is another topic for another day.