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In arithmetic, a quotient (from Latin: quotiens 'how many times', pronounced / ˈkwoʊʃənt /) is a quantity produced by the division of two numbers. [1] The quotient has widespread use throughout mathematics. It has two definitions: either the integer part of a division (in the case of Euclidean division) [2] or a fraction or ratio (in the ...
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations ...
Quotient (universal algebra) In mathematics, a quotient algebra is the result of partitioning the elements of an algebraic structure using a congruence relation . Quotient algebras are also called factor algebras. Here, the congruence relation must be an equivalence relation that is additionally compatible with all the operations of the algebra ...
Quotient group. A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo n can be obtained from the group of integers ...
Glossary of mathematical symbols. A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various ...
lim Δ P → 0 {\displaystyle \lim _ {\Delta P\rightarrow 0}\,\!} ), then ΔF (P) is known as an infinitesimal difference, with specific denotations of dP and dF (P) (in calculus graphing, the point is almost exclusively identified as "x" and F (x) as "y"). The function difference divided by the point difference is known as "difference quotient":
Algebraic expression. In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations ( addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number ). [1] For example, 3x2 − 2xy + c is an algebraic expression.
Congruence relation. In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. [1]
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