Injective example sentences

"Injective" Example Sentences

1. The function, being injective, maps distinct elements to distinct images.
2. It's crucial to verify if the transformation is truly injective before proceeding.
3. An injective mapping guarantees uniqueness in the codomain.
4. Mathematically speaking, an injective function is one-to-one.
5. Determining whether a function is injective is a common task in abstract algebra.
6. The proof hinges on showing the function's injective nature.
7. His argument failed because he neglected the condition of injectivity.
8. The theorem only holds for injective homomorphisms.
9. We can conclude that the given transformation is not injective.
10. For an injective function, the pre-image is unique.
11. The injectivity of this map is readily apparent.
12. A simple counterexample demonstrates the lack of injectivity.
13. Injective functions are essential in cryptography.
14. This problem requires a deep understanding of injective mappings.
15. The concept of injective functions is fundamental in set theory.
16. Is the proposed algorithm guaranteed to be injective?
17. The algorithm ensures an injective mapping of data points.
18. Proving injectivity is often more challenging than proving surjectivity.
19. We need to show that the function f is injective and surjective.
20. The horizontal line test is a useful tool for visualizing injectivity.
21. One-to-one correspondence is synonymous with being injective and surjective.
22. The proof relies on demonstrating the injectivity of the logarithm.
23. The condition for injectivity is satisfied in this specific case.
24. Only injective linear transformations are invertible.
25. Understanding injective functions simplifies many mathematical proofs.
26. The function is injective if and only if its kernel is trivial.
27. This is a classic example of a non-injective function.
28. The mapping is clearly injective, as demonstrated by this diagram.
29. If the function is injective, then we can define its inverse.
30. A necessary but not sufficient condition is that the function be injective.
31. The argument rests on the assumption of injectivity, which may not hold.
32. Because the function is injective, we can uniquely recover the input.
33. To prove injectivity, we'll use the contrapositive method.
34. The injective property ensures no information loss.
35. Is this transformation injective for all values of x?
36. Several theorems rely on the function being injective or surjective.
37. The question of injectivity is paramount in this context.
38. Let's assume, for the sake of argument, that the function is injective.
39. The proof of injectivity is straightforward in this case.
40. The failure of injectivity invalidates the previous conclusion.
41. We'll examine the injective nature of the map later in the proof.
42. The concept of injectivity is crucial in many areas of mathematics.
43. The mapping is both injective and surjective, hence bijective.
44. Verifying injectivity is often the hardest part of the problem.
45. The function's injective property allows for a unique solution.
46. Many advanced mathematical concepts depend upon the notion of an injective map.
47. This particular type of function is always injective.
48. We can use the definition of an injective function to solve this.
49. The problem reduces to showing that the function is injective.
50. Demonstrating injectivity is a prerequisite for proving the main theorem.