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> | ||
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| + | ==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.
Examples of bijective functions:
- such that , , and
Resources
- Course Textbook, pages 154-164
