Relative change and differenceIn any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a standard or reference or starting value. The comparison is expressed as a ratio and is a unitless number. By multiplying these ratios by 100 they can be expressed as percentages so the terms percentage change, percent(age) difference, or relative percentage difference are also commonly used.
Distributive propertyIn mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality is always true in elementary algebra. For example, in elementary arithmetic, one has Therefore, one would say that multiplication distributes over addition. This basic property of numbers is part of the definition of most algebraic structures that have two operations called addition and multiplication, such as complex numbers, polynomials, matrices, rings, and fields.
Subscript and superscriptA subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, while superscripts are above. Subscripts and superscripts are perhaps most often used in formulas, mathematical expressions, and specifications of chemical compounds and isotopes, but have many other uses as well.
Associative propertyIn mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs. Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed.
ModuloIn computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another (called the modulus of the operation). Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. For example, the expression "5 mod 2" would evaluate to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0; there is nothing to subtract from 9 after multiplying 3 times 3.
Parity (mathematics)In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is a multiple of two, and odd if it is not. For example, −4, 0, 82 are even because By contrast, −3, 5, 7, 21 are odd numbers. The above definition of parity applies only to integer numbers, hence it cannot be applied to numbers like 1/2 or 4.201. See the section "Higher mathematics" below for some extensions of the notion of parity to a larger class of "numbers" or in other more general settings.
IntegerAn integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold . The set of natural numbers is a subset of , which in turn is a subset of the set of all rational numbers , itself a subset of the real numbers . Like the natural numbers, is countably infinite.
Irreducible fractionAn irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). In other words, a fraction a/b is irreducible if and only if a and b are coprime, that is, if a and b have a greatest common divisor of 1. In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials.
Identity elementIn mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often shortened to identity (as in the case of additive identity and multiplicative identity) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.
Negative numberIn mathematics, a negative number represents an opposite. In the real number system, a negative number is a number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset. If a quantity, such as the charge on an electron, may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative.
