What does it mean for a set to be injective?

The injectivity of a function ensures a one-to-one correspondence between elements of the domain (set A) and a subset of the codomain (set B). It prohibits the occurrence of multiple elements in set A pointing to the same element in set B.

Conversely, the injective property also implies that no element in set B can be the target of more than one element from set A under the function's mapping. This restriction on the function's behavior maintains the integrity of the one-to-one relationship.

The importance of injective functions lies in their ability to preserve distinctness. They are useful in various mathematical and computational contexts, where preserving the unique identity of elements is crucial.

The concept of an injective function is a fundamental principle in mathematics, particularly in the realm of set theory. When a function maps elements from set A to set B, it is said to be injective if it satisfies a specific condition.

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