What are elements of a field called From Linear Algebra by Serge Lang we have

"Let K be a field. Elements of K will also be called
  numbers (without specification) if the reference to K is made clear by the context, or they will be called scalars."

What is the meaning of "if the reference to K is made clear by the context"? Is in this context the term numbers equivalent to scalars? Are there any difference between numbers and scalars in general?

In Linear Algebra, we can sometimes use vector spaces whose elements "look" just like scalars.  For example:

Define the vector space $V \subseteq \mathbb{R}^+$ with:

*

*Addition: $x+y = xy$

*Scalar multiplication: $rx = x^r$

Clearly, we could call $x$, $y$, and $r$ "numbers."  Yet, in this context, it is unclear which numbers are vectors and which are scalars.  So, we call $x$ and $y$ vectors and $r$ a scalar.  This is what is meant by "when it cannot be determined by context."
