Examples of 'injective' in a sentence
Meaning of "injective"
Referring to a function in mathematics where each element of the domain maps to a distinct element in the codomain
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- of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic
How to use "injective" in a sentence
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injective
Injective modules are defined dually to projective modules.
The composition of two injective functions is injective.
The injective hull of an injective module is itself.
A function f with a left inverse is necessarily injective.
We must show that it is injective and surjective.
The sequence is exact if and only if f is injective.
Every embedding is injective and continuous.
If then for any since the are injective.
If the function is injective the original can be reconstructed.
A function is bijective if it is both injective and surjective.
Our function f is injective because each element is distinct.
If is infinite then the function can be assumed to be injective.
A bijective function is an injective surjective function.
Isometries are always continuous and injective.
A continuous function is injective if and only if it is strictly monotonic.
See also
Thus the term universally injective.
An immediate corollary is that an injective cellular automaton must be surjective.
A function is called an embedding if it is both monotone and injective.
New spheres for application of injective medicinal forms.
Injective if and only if it is surjective.
It is not difficult to show that f is injective.
Every indecomposable injective module has a local endomorphism ring.
Return whether this morphism is injective.
Neither injective nor surjective.
Therefore the composite function f is injective.
Our injective gel technology.
The only remaining task is to show that is injective.
Then any morphism in which is injective on underlying sets is a monomorphism.
There are multiple other methods of proving that a function is injective.
Every direct sum of finitely many injective modules is injective.
So that is the case when we say the function is injective.
An injective function is an injection.
In algebra a monomorphism is an injective homomorphism.
The injective dimension of a module is the shortest length of an injective resolution.
A simple module is necessarily the socle of its injective hull.
An embedding of into is an injective map which is a homeomorphism onto its image.
All these morphisms are injective.
Functions which are both injective and surjective are also called bijective.
The dual notion of a projective object is that of an injective object.
The local homomorphisms are all injective for a covering by contractible open sets.
Let us show that it is injective.
An automaton that is both injective and surjective is called a reversible cellular automaton.
Thus a bijection is a function which is both injective and surjective.
This and other analogous injective functions from substructures are sometimes called natural injections.
We need to prove that it is injective.
The four possible combinations of injective and surjective features are illustrated in the adjacent diagrams.
The logarithmic function is injective.
The injective objects in Met are called injective metric spaces.
It is an example of an injective metric.
There is no injective function from X to the set of natural numbers.
