Examples of 'is injective' in a sentence
Meaning of "is injective"
is injective - In mathematics, particularly in the context of functions, injective refers to a type of function where each element of the domain maps to a unique element in the codomain
How to use "is injective" in a sentence
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is injective
We must show that it is injective and surjective.
The composition of two injective functions is injective.
Every embedding is injective and continuous.
The sequence is exact if and only if f is injective.
If the function is injective the original can be reconstructed.
It is not difficult to show that f is injective.
Our function f is injective because each element is distinct.
Return whether this morphism is injective.
A continuous function is injective if and only if it is strictly monotonic.
Therefore the composite function f is injective.
Is injective if and only if it is surjective.
The only remaining task is to show that is injective.
Then any morphism in which is injective on underlying sets is a monomorphism.
Every direct sum of finitely many injective modules is injective.
Hence and is injective.
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There are multiple other methods of proving that a function is injective.
Hence θ is injective.
So that is the case when we say the function is injective.
Which is injective.
We need to prove that it is injective.
Hence, function f is injective but not surjective.
The logarithmic function is injective.
Equivalently, a function is injective if it maps distinct arguments to distinct images.
Let us show that it is injective.
If M is flat, f is injective and so is an isomorphism onto its image.
Every embedding is injective.
A family contains any element exactly once, if and only if the corresponding function is injective.
Prove that ϕ is injective.
The homomorphism f is injective if and only if its kernel is only the singleton set { 0R.
Where defined it is injective.
DFX is injective we say that f is an immersion ( resp . local immersion ).
Equality holds if f is injective.
Here, the last map is injective by flatness and that gives us 1.
Every morphism in a concrete category whose underlying function is injective is a monomorphism.
Proof . ( i ) We will prove that is injective which will imply the injectivity of.
Any productive set has a productive function that is injective and total.
T is injective if and only if T ∗ is surjective ;.
Hence function is injective.
The representation ρ { \ displaystyle \ rho } is said to be faithful if it is injective.
Therefore h is injective.
In concrete categories, a function that has a left inverse is injective.
Now suppose that T is injective and surjective.
The enveloping von Neumann algebra is injective.
More generally, an abelian group is injective if and only if it is divisible.
In particular, if is a field then the Frobenius endomorphism is injective.
Therefore, n is injective.
Consequently, the range of N is dense if and only if N is injective.
There is a function f, A → A that is injective but not surjective.
Therefore it follows from the definition that " ƒ " is injective.
Consequently, h is injective.
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Examples of using Injective
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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
