## One-to-One

Let be a Function defined on a Set and taking values in a set . Then is said to be one-to-one (a.k.a. an Injection or Embedding) if, whenever , it must be the case that . In other words, is one-to-one if it Maps distinct objects to distinct objects.

If the function is a linear Operator which assigns a unique Map to each value in a Vector Space, it is called one-to-one. Specifically, given a Vector Space with , then a Transformation defined on is one-to-one if for all .