These are all examples of multivalued functions that come about from non-injective functions.
2.
Any injective function between two finite sets of the same cardinality is also a surjective function ( a surjection ).
3.
The identity function on is clearly an injective function as well as a surjective function, so it is also bijective.
4.
In whole-world presentation, the back and front hemispheres overlap, making the projection a non-injective function.
5.
The integers are countable because the function given by if is non-negative and if is negative, is an injective function.
6.
In classical mathematics, every injective function with a nonempty domain necessarily has a left inverse; however, this may fail in constructive mathematics.
7.
*PM : properties of injective functions, id = 8879 new !-- WP guess : properties of injective functions-- Status:
8.
*PM : properties of injective functions, id = 8879 new !-- WP guess : properties of injective functions-- Status:
9.
It cannot be strictly increasing, as if it were we would have an injective function from the ordinals into a set, violating Hartogs'lemma.
10.
There is a natural injective function from an affine space into the set of prime ideals ( that is the spectrum ) of its ring of polynomial functions.
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