Appendix: Mathematical symbol glossary

This page illustrates the most common mathematical symbols you are likely to encounter. If any course uses a notation not on this page you should expect it to have been previously defined in that course. Otherwise you should feel no hesitation in requesting an explanation (or to ask me to include it in this glossary!).

$\alpha, \beta, \gamma, \delta$	greek letters
$\mbox{A}, \mbox{B}, \Gamma, \Delta$	upper case greek letters
0, 1, -2, 3.14159	numbers
$+, -, \times, /$	arithmetic operators
$<, >, \geq, =$	relational operators
$\wedge, \vee, \neg, \Rightarrow, \Leftrightarrow$	logical operators
$\forall, \exists$	logical quantifiers (`for all', `there exists')
$\{\}$, $\{3,5,7\}$, $\{x \mid x^2-3x+2=0 \}$	sets
$\cap, \cup, \times, \rightarrow$	set operators
	(intersection, union, cartesian product, function space)
$\subseteq, \supseteq, =$	set relational operators
$\in$	set membership
|S|	number of members in set S
${\cal P}(S)$	power set of S (set of all subsets)
$\mbox{I$\!$ N}, \mbox{Z$\!\!\!$ Z}$	natural numbers (0,1,2,...), integers
$\lambda x.x+1$	anonymous function.

Sometimes, as for induction, $A \wedge B \Rightarrow C$ is written (but beware this as a sloppy explanation):

$$\frac{A\hspace{2em}B}{C}$$

Examples (some of these are definitions of the corresponding symbols):

$$\begin{eqnarray*}x > 5 &\Rightarrow& x^2 > 16 \\ x^2 \ge 9 &\Leftrightarrow& (x... ...N}&\Rightarrow& n+1 \in \mbox{I$\!$ N}\\ (\lambda x.x+1)5 &=& 6 \end{eqnarray*}$$

Mathematical induction can be summarised as:

$$\frac{P(0)\hspace{5em}P(k) \Rightarrow P(k+1)}{(\forall n\in \mbox{I$\!$ N})P(n)}$$