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Injection (mathematics): Difference between revisions
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(Created page with "== Definition == In the field of mathematics, an injection (also known as an injective function or one-to-one function) is a function that maps distinct elements of its domain to distinct elements of its codomain. In simpler terms, an injective function does not map different elements to the same element. This concept is fundamental in many areas of mathematics, including set theory, algebra, and topology. == Forma...") |
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Formally, a function ''f'' from a set ''X'' to a set ''Y'' is defined as injective if for every ''x1'' and ''x2'' in ''X'', whenever ''f(x1) = f(x2)'', then ''x1 = x2''. This definition can also be written in the contrapositive form: if ''x1 ≠ x2'', then ''f(x1) ≠ f(x2)''. | Formally, a function ''f'' from a set ''X'' to a set ''Y'' is defined as injective if for every ''x1'' and ''x2'' in ''X'', whenever ''f(x1) = f(x2)'', then ''x1 = x2''. This definition can also be written in the contrapositive form: if ''x1 ≠ x2'', then ''f(x1) ≠ f(x2)''. | ||
[[Image:Detail-77809.jpg|thumb|center|A visual representation of an injective function. It shows a set X and a set Y with arrows from each element in X to a unique element in Y.]] | |||
== Properties of Injective Functions == | == Properties of Injective Functions == | ||