Horizontal Line Test in Set Theory
Consider a function with its corresponding graph as a subset of the Cartesian product . Consider the horizontal lines in :. 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.
A horizontal line is a straight line going right. A vertical line, however, is upwards (perpendicular mostly). Variations of the horizontal line test can be used to determine whether a function is surjective or bijective:
- The function f is surjective (i.e., onto) if and only if its graph intersects any horizontal line at LEAST once.
- f is bijective if and only if any horizontal line will intersect the graph EXACTLY once.
- Vertical line test
- Function (mathematics)
- Inverse (mathematics)
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