A notational system is a means of unambiguously expressing a certain relationship between, or certain properties of, one or more quantities under investigation. Such a system makes use of written symbols that either represent the quantities in question or connect them to each other in various ways. The former kinds of symbols are referred to as variables, quantities, or terms, and the latter symbols are referred to as operators, predicates, or connectives. Generally speaking, variables represent the specific “things” we are making reference to, and operators and connectives express the relationships between these things. A specific sequence of these symbols is called a mathematical expression and is restricted by rules that set the syntax of allowable expressions. Those combinations of symbols that have correct syntax in a given notational system are called well-defined, and those that don’t are generally considered nonsensical and aren’t pursued further. For example, the expressions 1+1=2 and 2×2=4 are well-defined relative to the almost universal notational system of basic arithmetic, but expressions such as ×2+=1 are syntactically incorrect. These rules of syntax are largely a matter of convention, and it is possible to envision a notational system where this last “incorrect” expression is accepted as possessing a clear meaning.
Miller, Jacob, "The Adumbrant Notational System" (2011). 2011 AHS Capstone Projects. 15.