The following list contains all predefined statements (formulas) and object expressions (terms) together with (typical) corresponding textbook expressions.
Formulas
| \(\LaTeX\) | \(\small\mathbb M\)ATh | comment |
| \(E\wedge F\) | E and F | |
| \(E\vee F\) | E or F | |
| \(E\Rightarrow F\) | E => F | |
| \(E\Leftrightarrow F\) | E <=> F | |
| \(\neg E\) | not(E) | |
| \(x=y\) | x = y | |
| \(x\neq y\) | x /= y | |
| \(x\in U\) | x : U | |
| \(x\notin U\) | x /: U | |
| \(U\subseteq V\) | U c= V | |
| \(\forall p\in U: E\) | [forall p:U holds E] | variants |
| \(\exists p\in U: E\) | [exists p:U sothat E] | variants |
| \(\exists! p\in U: E\) | [exists! p:U sothat E] | variants |
| \(\exists_{\leq 1} p\in U: E\) | [! p:U sothat E] | variants |
| \(\top\) | tautology | |
| \(\bot\) | contradiction |
Terms
| \(\LaTeX\) | \(\small\mathbb M\)ATh | comment |
| \(\mathbb N_0\) | Nat0 | |
| – | Element | all elements |
| – | Set | all sets |
| – | Function | all functions |
| – | Basic | all basic elements |
| \(42\) | 42 | decimal representations |
| \((38,50,50,47)\) | "cool" | strings |
| \(\{3,8,2,11\}\) | {3,8,2,11} | |
| \(\emptyset\) | { } | |
| \((3,8,2,11)\) | [3,8,2,11] | |
| \(\{p\in U:E\}\) | {p:U sothat E} | variants |
| \(\{y\,|\,p\in U\}\) | {y for p:U} | variants |
| \((y)_{p\in U}\) | [y for p:U] | variants |
| \(U\backslash V\) | U\V | set difference |
| \(U\to V\) | U --> V | |
| \(U\rightharpoonup V\) | U -->> V | partial functions |
| \(U^n\) | U^n | tuple |
| \(\mathcal P(U)\) | pow(U) | power set |
| \(\bigcup_{p:U}V\) | union(V for p:U) | variants |
| \(\bigcap_{p:U}V\) | sec(V for p:U) | variants |
| \(\prod_{p:U}V\) | prd(V for p:U) | variants |
| \(\textrm{dom}(f)\) | dom(f) | |
| \(\textrm{img}(f)\) | img(f) | |
| \(f(x)\) | f(x) | function evaluation |
| \(\iota x\in U:E\) | [the x:U sothat E] | definite description |
| – | entry(U) | element of a singleton |