Editing Mathematical notation (section)

== Meaning and interpretation ==
The [[syntax]] of notation defines how symbols can be combined to make [[Expression (mathematics)#Well-defined expressions|well-formed expressions]], without any given meaning or interpretation. The [[semantics]] of notation interprets what the symbols represent and assigns a meaning to the expressions and formulas. The reverse process of taking a statement and writing it in logical or mathematical notation is called [[Logic translation|translation]]. 

=== Interpretation ===
Given a [[formal language]], an [[Interpretation (logic)|interpretation]] assigns a [[domain of discourse]] to the language. Specifically, it assigns each of the constant symbols to objects of the domain, function letters to functions within the domain, predicate letters to statments, and vairiables are assumed to range over the domain.

=== Map–territory relation ===
The [[map–territory relation]] describes the relationship between an object and the representation of that object, such as the [[Earth]] and a [[map]] of it. In mathematics, this is how the number 4 relates to its representation "4". The quotation marks are the formally correct usage, distinguishing the number from its name. However, it is fairly common practice in math to commit this falacy saying "Let x denote...", rather than "Let "x" denote..." which is generally harmless.