In the case of a dyadic relation that has the qualifications of a function
there are a number of further differentia that arise:
For example, the function depicted below is neither total nor tubular at its codomain
so it can enjoy none of the properties of being surjective, injective, or bijective.
![]() |
(40) |
An easy way to extract a surjective function from any function is to reset its codomain to its range. For example, the range of the function above is
Thus, if we form a new function
that looks just like
on the domain
but is assigned the codomain
then
is surjective, and is described as a mapping onto
![]() |
(41) |
The function is injective.
![]() |
(42) |
The function is bijective.
![]() |
(43) |
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