bijektiftir

Bijektiftir is a mathematical term used in Turkish to describe a property of a function. A function f from a set A to a set B is said to be bijektif (bijective) when it is both injective (one-to-one) and surjective (onto). In other words, each element of A is mapped to a unique element of B, and every element of B is the image of some element of A. This creates a one-to-one correspondence between A and B and typically allows the existence of an inverse function f^{-1}: B → A.

Injective means that different inputs map to different outputs: if a1 ≠ a2 in A, then f(a1) ≠ f(a2). Surjective means that every element of the codomain B is achieved by some input from A: for every b in B, there exists an a in A with f(a) = b. A function that is both injective and surjective is bijektif.

Consequences and examples: A bijective function has a unique inverse function. Therefore domain and codomain have a precise one-to-one pairing, and in the finite case they share the same cardinality. Example: f: {1,2,3} → {a,b,c} defined by f(1)=a, f(2)=b, f(3)=c is bijektif; its inverse maps a→1, b→2, c→3. Another common bijection is f: R → R with f(x) = 2x, whose inverse is f^{-1}(y) = y/2. By contrast, f(x) = x^2 on R is not bijektif, since it is not injective and not surjective onto all real numbers.

Usage: In Turkish mathematical writing, the phrase “f bijektiftir” states that a given function f is bijektif, emphasizing the existence of a two-way correspondence between the sets involved.