Rational Number

A rational number is a Number generated by the ratio of two integers, where the Denominator is not 0.

• Context:
  • It can be a member of the Rational Number Set.
  • It can range from being a Negative Rational Number to being a Non-Negative Rational Number to being a Non-Positive Rational Number to being a Positive Rational Number.
• Example(s)
  • any Integer Number, such as [math]\displaystyle{ ..., -\frac{1}{1}, \frac{0}{1}, \frac{1}{1}, ... }[/math]
  • a Positive Rational Number, such as ..., ⅛, ¼, ⅓, ½, ⅜ ⅝, ⅔, ¾, ⅞, ...
  • a Negative Rational Number, such as [math]\displaystyle{ -\frac{1}{2} }[/math]
• Counter-Example(s):
  • an Irrational Number, such as [math]\displaystyle{ \sqrt{2} }[/math] or [math]\displaystyle{ \frac{1}{\pi} }[/math].
• See: Dirichlet Function.

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References

2011

• http://en.wikipedia.org/wiki/Rational_number
  • In mathematics, a rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator [math]\displaystyle{ b }[/math] not equal to zero. Since [math]\displaystyle{ b }[/math] may be equal to 1, every integer is a rational number. The set of all rational numbers is usually denoted by a boldface Q (or blackboard bold [math]\displaystyle{ \mathbb{Q} }[/math], Unicode U+211a ℚ), which stands for quotient.
  • The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over. Moreover, any repeating or terminating decimal represents a rational number. These statements hold true not just for base 10, but also for binary, hexadecimal, or any other integer base.

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