From Citizendium, the Citizens' Compendium
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- Absorbing element : An element whose behaviour with respect to an algebraic binary operation is like that of zero with respect to multiplication.
- Addition : A binary mathematical operation of summing numbers or quantities together.
- Algebra over a field : A ring containing an isomorphic copy of a given field in its centre.
- Algebra : A branch of mathematics concerning the study of structure, relation and quantity.
- Associativity : A property of an algebraic operation such as multiplication: a(bc) = (ab)c.
- Binary operation : A function of two elements within a set, which assigns another value from among the elements of the set.
- Commutativity : A property of a binary operation (such as addition or multiplication), that the two operands may be interchanged without affecting the result.
- Distributivity : A relation between two binary operations on a set generalising that of multiplication to addition: a(b+c)=ab+ac.
- Division (arithmetic) : The process of determing how many copies of one quantity are required to make up another; repeated subtraction; the inverse operation to multiplication.
- Elementary function : Mathematical functions built from a finite number of exponentials, logarithms, constants, one variable, and roots of equations through composition and combinations using the four elementary arithmetic operations (+ – × ÷).
- Euclid's lemma : A prime number that divides a product of two integers must divide one of the two integers.
- Fraction (mathematics) : A concept used to convey a proportional relation between a part and the whole consisting of a numerator (an integer — the part) and a denominator (a natural number — the whole).
- Group (mathematics) : Set with a binary associative operation such that the operation admits an identity element and each element of the set has an inverse element for the operation.
- Identity element : An element whose behaviour with respect to a binary operation generalises that of zero for addition or one for multiplication.
- Integer : The positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero.
- Linear equation : Algebraic equation, such as y = 2x + 7 or 3x + 2y − z = 4, in which the highest degree term in the variable or variables is of the first degree.
- Mathematics : The study of quantities, structures, their relations, and changes thereof.
- Monoid : An algebraic structure with an associative binary operation and an identity element.
- Natural number : An element of 1, 2, 3, 4, ..., often also including 0.
- Pi (Greek letter) : The sixteenth letter of the Greek alphabet, written as (upper-case) and (lower-case).
- Pointwise operation : Method of extending an operation defined on an algebraic struture to a set of functions taking values in that structure.
- Polynomial : A formal expression obtained from constant numbers and one or indeterminates; the function defined by such a formula.
- Prime number : A number that can be evenly divided by exactly two positive whole numbers, namely one and itself.
- Real number : A limit of the Cauchy sequence of rational numbers.
- Semigroup : An algebraic structure with an associative binary operation.
- Sequence : An enumerated list in mathematics; the elements of this list are usually referred as to the terms.
- Tetration : Holomorphic function characterized in that at integer values of its argument it can be interpreted as iterated exponent.