1-1 corospondence

**Chris11** · February 17th 2010, 10:03 PM

Hi. I have a problem that invovles proving a one to one corospondence. How do you go about proving the corospondence?

**Drexel28** · February 17th 2010, 10:05 PM

Originally Posted by Chris11

Hi. I have a problem that invovles proving a one to one corospondence. How do you go about proving the corospondence?

$f:X\mapsto Y\text{ is injective }\Leftrightarrow \left(f(x)=f(y)\implies x=y\right)\Leftrightarrow\left(x\ne y\implies f(x)\ne f(y)\right)$

**Roam** · February 17th 2010, 11:38 PM

In words, if different inputs always give different outputs. More formally, If we suppose $f: A \rightarrow B$ has the property that if $a,a' \in A$ and $a \neq a'$ , then $f(a) \neq f(a')$ . We say $f$ is 1-1 or injective or monic.

Another way of saying that is to observe that $\forall a,a' \in A$ , if $f(a)=f(a')$ then $a = a'$ .

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