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
- algebraic number
- A number that can be the solution of an
algebraic equation; a number that is not
- A fixed process which, if carried out systematically,
produces a desired result.
- 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.
- Short for binary digit. One digit in the binary representation
of a number.
- Eight bits
- binary notation
- The representation of integers in terms of powers
- The mathematical 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
- 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.
- 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.
- An association between the elements of two sets.
More formally, a formula by which such an association can be computed.
- 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.
- A number from which another number is subtracted. For example, in 5 − 3 = 2, 5 is the minuend.
- 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. See congruences.
- The number that is multiplied by another. For example, in 3 × 2 = 6, 3 is called the multiplicand.
- The number by which another number is multiplied. For example, in 3 × 2 = 6, 2 is called the multiplier.
- natural number
- A positive integer. See the link for more details.
- 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. See the link for more details.
- The result of multiplying two numbers together.
- real number
- Any finite or infinite decimal. Any rational or
- The remainder upon division of one integer by another.
- A number subtracted from another number. For example, in 5 − 3 = 2, 3 is the subtrahend.
- 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 19th 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).