## Maths Glossary

**Please turn javascript on.**

also see

Algs&DS

MML

ProgLangs

FP

logic

semantics

**Application**, f(x), of a function, f, to an actual parameter, x. May also be written as f x, or as postfix, x f, or even as x^{f}. Also see*composition*.**Associative**, where a binary operation, '·', satisfies (a · b) · c = a · (b · c), e.g., addition (+) of integers (but*not*subtraction (-)).**Commutative**, where a binary operation, '·', satisfies a · b = b · a, for all appropriate a and b, e.g., addition (+) of integers.**Composition**, f·g, of functions g:X→Y and f:Y→Z, (f·g)(x) = f(g(x)), f·g:X→Z; apply g first and then f. Note that composition is associative, (f·g)·h = f·(g·h). (f·g is sometimes written as fg, and sometimes as postfix g;f, or even gf!) Also see*application*.**Graph**, see [here].**Group**, see [here].**iff**, short for "if and only if," ⇔.**s.t.**, short for "such that".**N**, the natural numbers, {0, 1, 2, 3, ... }.**Q**, the rational numbers, {m/n | m∈**Z**, n∈**N**-{0}}.**R**, the real numbers. (Can't enumerate them!)**S**_{n}, the*symmetric group*(of permutations) over {1,...,n}.**Z**, the integers, { ..., -2, -1, 0, 1, 2, 3, ... }.**Z**_{n}, the integers modulo (mod) n, {0, 1, ..., n-1}.**Z**_{p}, as above, {0, 1, ..., p-1}, where p is a prime number.- ∀, for all; also see [logic] and [spec.chars].
- ∃, there exists.
- ∧, as in p∧q, p and q, conjunction.
- ∨, as in p∨q, p or q, disjunction.
- ¬, as in ¬p, not p, logical negation.
- ∈, as in x∈S, x is a member of S.
- ∩, as in S∩T, set intersection.
- ∪, as in S∪T, set union.
- |x|, the size of x, the length of a sequence or string, the number of elements in a set, etc..
- [y,z] = {x | y ≤ x ≤ z}, closed interval.
- [y,z) = {x | y ≤ x < z}, half closed interval.
- (y,z] = {x | y < x ≤ z}, half closed interval.
- (y,z) = {x | y < x < z}, open interval
(but also
*unordered pair*in other contexts). - ⟨x, y⟩, ordered pair, note ⟨x, y⟩ ≠ ⟨y, x⟩ in general.
- {x | p(x)}, the set of x such that p(x) is true.

**Please turn javascript on.**