Definition of "totient" I had always taken the term "totient" to be defined by saying that the totient of a positive integer $n$ is the number of positive integers less than $n$ that are coprime to $n$.  Thus, for example, the totient of $10$ is $4$.
In a discussion under this question, someone suggests, without being very explicit, that "the totients of $n$" are those positive integers less than $n$ and coprime to $n$.  By that definition, the totients of $10$ would be $1,3,7,9$.  (He has since edited his answer so that it no longer uses the word "totient".)
Am I the only one not aware of the second definition, or is the person who said that the only person who was aware of it?  Or might some other alternative be true?
 A: 
Am I the only one not aware of the second definition[?]

Of course not.  Most people don't know any definition of "totient", including a positive proportion (it is not implausible that the proportion may exceed $\frac{1}{2}$) of mathematicians.

[O]r is the person who said that the only person who was aware of it?

Among the billions of people in the world, is there someone else who uses "totient" to mean the set of reduced residues modulo $n$ (or an element of that set) rather than its cardinality?  It seems overwhelmingly probable, but I don't know of an explicit example.
I think these questions are not very fruitful.  Let's instead ask: is it standard to define the totient as the set of reduced residues modulo $n$ (or an element of that set)?  No, it is not.   I am a number theorist, and I have never encountered this alternative definition.  
Let me reiterate though that the proportion of the mathematical community which does not know any definition for "totient" is large and growing.  In much contemporary writing the word simply isn't used: rather one says Euler's $\varphi$ function.  If you are going to use the word "totient" in any context, it would be safest to give the definition or at least drop the keywords "Euler" and "$\varphi$".
