Explanation
1. Definition of a One-One (Injective) Function: A function f from set A to set B (f:A→B) is called a one-one function or an injective function if no two distinct elements in the domain (Set A) share the exact same image in the codomain (Set B).
In simple terms, unique inputs must produce unique outputs.
2. Mathematical Expression: Mathematically, a function is one-one if and only if:
For any x1,x2∈A, if f(x1)=f(x2)⟹x1=x2
Alternatively, using its contrapositive statement:
If x1=x2⟹f(x1)=f(x2)
This precisely translates to: "Different elements of A have different images in B."
