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# One - One Watch

1. How do you show functions are one to one

eg

2. I'd imagine you'd do it by performing a formula that my non-mathmatical mind can't conquer. ):
3. f isn't one-to-one. f(1)=f(-7)=17.
4. That function is not injective. (In other words, there are two distinct numbers x and y such that .)
5. Just sketch the graph, it should then be pretty clear whether the function is 1:1 or not.
6. A function is injective (a.k.a. "1-1") if whenever , . That is, distinct points are mapped to distinct points. Equivalently, it's injective if implies that .

So for example isn't injective, since but .

However, is injective, since if then , so .

A good way of telling if a map is injective is to draw a graph. If you held an infinitely long ruler horizontally anywhere over the graph, it should only ever intersect the graph at one point. Otherwise, it's not injective.

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Updated: December 17, 2010
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