Difference between revisions of "Functions:Bijective"
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(Created page with "A function is bijective if it is both injective and surjective. That is, a bijective function maps each element of the domain to a distinct element in the codomain, and every...") |
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[[File:Injective, Surjective, Bijective.svg|Injective, Surjective, and Bijective arrow diagrams]] | [[File:Injective, Surjective, Bijective.svg|Injective, Surjective, and Bijective arrow diagrams]] | ||
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| + | Examples of bijective functions: | ||
| + | * <math> f:A\to B, A = \{a, b, c\}, B = \{1, 2, 3\}</math> such that <math> f(a) = 1 </math>, <math> f(b) = 2 </math>, and <math> f(c) = 3 </math> | ||
| + | * <math> f:\R\to\R, f(x) = 3x + 5 </math> | ||
| + | * <math> f:\R\to\R, f(x) = x^3 </math> | ||
| + | |||
| + | ==Resources== | ||
| + | * [https://link-springer-com.libweb.lib.utsa.edu/content/pdf/10.1007%2F978-1-4419-7127-2.pdf Course Textbook], pages 154-164 | ||
Revision as of 14:52, 27 September 2021
A function is bijective if it is both injective and surjective. That is, a bijective function maps each element of the domain to a distinct element in the codomain, and every element in the codomain is mapped to by exactly one element of the domain.
Injective, Surjective, and Bijective arrow diagrams
Examples of bijective functions:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f:A\to B, A = \{a, b, c\}, B = \{1, 2, 3\}} such that , , and
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f:\R\to\R, f(x) = x^3 }
Resources
- Course Textbook, pages 154-164
