Editing Quotient (section)

==Quotient of two integers==
{{Main|Rational number}}

A [[rational number]] can be defined as the quotient of two [[integer]]s (as long as the denominator is non-zero).

A more detailed definition goes as follows:<ref>{{Cite book |title=Discrete mathematics with applications |last=Epp |first=Susanna S. |date=2011-01-01 |publisher=Brooks/Cole |isbn=9780495391326 |oclc=970542319 |pages=163}}</ref>

: A real number ''r'' is rational, if and only if it can be expressed as a quotient of two integers with a nonzero denominator. A real number that is not rational is irrational.

Or more formally: 
: Given a real number ''r'', ''r'' is rational if and only if there exists integers ''a'' and ''b'' such that <math>r = \tfrac a b</math> and  <math>b \neq 0</math>.

The existence of [[irrational number]]s—numbers that are not a quotient of two integers—was first discovered in geometry, in such things as the ratio of the diagonal to the side in a square.<ref>{{Cite web|title=Irrationality of the square root of 2.|url=https://www.math.utah.edu/~pa/math/q1.html|access-date=2020-08-27|website=www.math.utah.edu}}</ref>