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 otherwords, 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 iscalled one-to-one. Specifically, given a Vector Space 
with 
, then aTransformation defined on is one-to-one if 
for all 
.
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