[228]In the definition [00G] we speak of atomic formulas, i.e. composed of a single variable; we want to reflect on this. In programming languages we may use names composed of several letters to identify objects (variables, functions, etc.): such as
foo = 3 ; bar = 7; foo = foo + bar;
In mathematics this is unusual, since in a formula such as
it would be difficult to understand if xyz is a variable, or the product of three variables \(x,y,z\). For this reason, usually, in mathematics the identifiers are composed of a single letter; some notable functions are an exception, such as \(\sin ,\cos ,\exp ,\log \)…etc. However, this creates some problems when you want to express a formula where there are many variables; for this reason, letters from the Greek alphabet are also used, and even Hebrew, in particular ”aleph” \(\aleph \) and ”beth” \(\beth \); and the letters are also accompanied by indexes, subscript as \(x_ 1,x_ 2,x_ 3\) or superscript \(x^ 1,x^ 2,x^ 3\) (being careful not to be confused with the exponentiation); then there are variants expressed with the signs \(\hat x,\overline x,\tilde x,x'\) (being careful not to get confused with derivatives); and there are choices of fonts, such as ”calligraphic” \(\mathcal A,\mathcal B,\mathcal C,\mathcal D,\ldots \), the ”fraktur” \(\mathfrak a,\mathfrak b,\mathfrak c,\mathfrak d\ldots \mathfrak A,\mathfrak B,\mathfrak C,\mathfrak D\) or the blackboard bold \(\mathbb a,\mathbb b,\mathbb c,\mathbb d\ldots \mathbb A,\mathbb B,\mathbb C,\mathbb D\).