Injektiivisyys
Injektiivisyys, also known as one-to-one or injective, is a fundamental property of functions in mathematics. A function is injective if each element in its codomain is mapped to by at most one element in its domain. In simpler terms, distinct inputs always produce distinct outputs. If we have a function f: A -> B, it is injective if for any two distinct elements x1 and x2 in set A, their images under f, f(x1) and f(x2), are also distinct. Mathematically, this is often expressed as: if f(x1) = f(x2), then x1 = x2.
Consider the function f(x) = 2x, where the domain and codomain are the set of real numbers. If
The concept of injectivity is crucial in various areas of mathematics, including set theory, abstract algebra,