Editing Horizontal line test (section)

==In set theory==
Consider a function <math>f \colon X \to Y</math> with its corresponding [[graph of a function|graph]] as a subset of the [[Cartesian product]] <math>X \times Y</math>. Consider the horizontal lines in <math>X \times Y</math> :<math>\{(x,y_0) \in X \times Y: y_0 \text{ is constant}\} = X \times \{y_0\}</math>. The function ''f'' is [[injective]] [[if and only if]] each horizontal line intersects the graph at most once. In this case the graph is said to pass the horizontal line test. If any horizontal line intersects the graph more than once, the function fails the horizontal line test and is not injective.<ref>{{cite book|last1=Zorn|first2=Arnold |last2=Ostebee |first1=Paul|title=Calculus from graphical, numerical, and symbolic points of view|year=2002|publisher=Brooks/Cole/Thomson Learning|location=Australia|isbn=0-03-025681-X|pages=185|url=https://books.google.com/books?id=D48RplvmxVUC&q=horizontal+line+test|edition=2nd|quote=No horizontal line crosses the f-graph more than once.}}</ref>