A theory is put forward here: as we work upward in a concept progression, each new concept includes the prior concepts and/or is capable of utilizing the prior concepts.
We start in Algebra with variables holding values.
Then we learn about functions, which take a value and return a value.
As an example f(x)=x+3 takes the value 2 and returns the value 5.
But a function could be a value, as for example, f(x)=6.
Next we learn that an operator takes a function and returns a function.
As an example, the operator d/dx takes the function x^2 and returns the function 2x.
But it is legal for operators to do simpler things like add 3, so an operator could be a function disguised as an operator, and that function could be a constant.
This process of more advanced items containing less advanced items happen again when we move along the following progression:
scalar –> vector –> matrix –> tensor
A vector in 1D space is like a scalar.
A matrix with one of the dimensions having a value of 1 is like a vector.
Textbooks introducing tensors identify scalars, vectors, and matrices as being tensors of different degrees: 0, 1, and 2 respectively. This could be what gave us the whole idea of Concept Progression.
Because of this progression, when we saw a definition for Algebraic Expression requiring there to be an operator, we were skeptical. We felt that a mixture of values and variables with an operator would provide a good example of what an algebraic expression could be, since it shows all possible features. But we felt that a single variable or a single value could also be algebraic expressions.
Someone might say a variable is required because an expression without a variable would be a mathematical expression.
Rob Sterling 