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Injection (mathematics): Difference between revisions
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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.]] | [[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.|class=only_on_mobile]] | ||
[[Image:Detail-77810.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.|class=only_on_desktop]] | |||
== Properties of Injective Functions == | == Properties of Injective Functions == | ||