Glossary

Note that some definitions are currently grouped in functional order, not alphabetical order. As well, this page is not complete.

abundant number

A number that is less than the sum of its factors (excluding itself). For example, the factors of 12 (1, 2, 3, 4, 6) add up to 16. Compare deficient number, perfect number.

algebraic number

A number that can be the solution of an algebraic equation; a number that is not transcendental.

algorithm

A fixed process which, if carried out systematically, produces a desired result.

axiom

A statement which is accepted as a basis for further logical argument. Generally axioms are self-evident truths or principles which are basic enough that there are no principles more basic from which to prove them.

bit

Short for binary digit. One digit in the binary representation of a number.

byte

Eight bits

binary notation

The representation of integers in terms of powers of two.

combinatorics

The mathimatical discipline which attempts to answer "how many" questions (without actually having to count).

complex number

A number of the form a + bi where a and b are real numbers and i is the square root of -1.

continuum hypothesis

See Continuum hypothesis page.

deficient number

A number whose proper factors sum up to less than the number itself. For example, the proper factors of 10 are 1, 2, and 5, which sum to 8.

factorial

See Factorial number page.

four-colour theorem

A theorem that states that it is always possible to colour a regular "map" with no more than four colours. This was proved in 1976. The proof used a computer in a way that was unique at that time.

function

An association between the elements of two sets. More formally, a formula by which such an association can be computed.

integer

The positive integers (natural numbers) are 1, 2, 3, ... . The negative integers are -1, -2, -3, ... . The integers include the positive integers, negative integers, and 0.

irrational number

A number that cannot be expressed as the ratio of two integers. The first irrational number to be discovered was the square root of 2. "Most" real numbers are irrational.

modulo

When integers are taken "modulo m", one neglects multiples of m and considers only the remainder. Therefore, 17 (modulo 5) = 2 because 17 = 5 x 3 + 2.

natural number

A positive integer.

perfect number

A number whose proper factors sum up to the number itself. For example, the proper factors of 6 are 1, 2, and 3, which sum to 6.

real number

Any finite or infinite decimal. Any rational or irrational number.

residue

The remainder upon division of one integer by another.

transcendental number

A number that is not algebraic, and so cannot be the solution of an algebraic equation. The first transcendental number was found by the French mathematician Joseph Liouville in the mid 19^th century. It is 0.1100010000000000000000010000... where 1's appear in the n!^th positions where n can be any natural number. Almost all numbers are transcendental (see a discussion of this).