What is Algebra?

Nature of Algebra 

Algebra is a set of finitely many symbols with functions and operators acting on these symbols in such a fashion that all these functions and operators can be implemented in an electro-mechanical device or a computer or computer program.

A human being or a machine, by applying mechanically oriented operations could simply operate on the symbols of an algebra without any requirements to understand what the symbols or the operations are supposed to mean!

The latter is called Abstraction.

Example: The Comma operator

a , b

separates the ‘a’ from ‘b’ so it is not confused with ‘ab’ or in general separates the Right Hand Side (rhs) from Left Hand Side (lhs).

Example: The Function Sin

Sin(a)

computes the well known trigonometric function Sinus.