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Examples of Injective functions


Injective functions

Post by natttt
Posted on 2011-05-05 10:25:40
A function f is injective if and only if whenever f(x) = f(y), x = y.


Example: f(x) = x+5 from the set of real numbers naturals to naturals is an injective function.

This function can be easily reversed. For example:
* f(3) = 8

Given 8 we can go back to 3


Example: f(x) = x2 from the set of real numbers naturals to naturals is not an injective function because of this kind of thing:
* f(2) = 4 and
* f(-2) = 4

This is against the definition f(x) = f(y), x = y, because f(2) = f(-2) but 2 ≠ -2

In other words there are two values of "A" that point to one "B", and this function could not be reversed (given the value "4" ... what produced it?)


BUT if we made it from the set of natural numbers naturals to naturals then it is injective, because:

* f(2) = 4
* there is no f(-2), because -2 is not a natural number


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