Inyectividad

Inyectividad, also known as injectivity or one-to-one, is a property of functions in mathematics. A function f from a set A to a set B is said to be injective if distinct elements in the domain A map to distinct elements in the codomain B. In other words, for any two elements x1 and x2 in A, if f(x1) = f(x2), then it must be true that x1 = x2. Conversely, if x1 is not equal to x2, then f(x1) cannot be equal to f(x2).

This property ensures that no two different inputs produce the same output. Visually, if you were to plot the graph of an injective function, any horizontal line would intersect the graph at most at one point. This is often referred to as the horizontal line test.

Injective functions are important in various areas of mathematics, including set theory, abstract algebra, and calculus. They are crucial for defining concepts like isomorphisms, which are structure-preserving bijections between mathematical objects. A function that is both injective and surjective (onto) is called bijective. Bijective functions have a unique inverse function. The concept of injectivity is fundamental to understanding how functions relate different sets of objects and preserves distinctions between them.