associative property

In mathematics, the associative property is a property of some binary operations.

The associative property is closely related to the commutative property.

They also follow commutative properties and associative properties, just like real numbers.

Long-term depression also works through associative properties although it is not always the reverse process of LTP.

(This is called the associative property.)

Owing to the above properties (along with the associative property, which rotations obey), the set of all rotations is a group under composition.

Note that the associative property does 'not' hold for expressions that include non-linear operators, such as the antilinear T-symmetry in physics.

In category theory, the associator expresses the associative properties of the internal product functor in monoidal categories.

(2) associative property:

A semigroup is a set together with a binary operation "" (that is, a function ) that satisfies the associative property:

This formula, which is the formula given on standardized tests such as the SAT,is developed as a connection to previous work with multiplication, area, and the associative property.

The first is focused on abstract mental functions of an intelligent mind and operates using symbols, and the second, which follows the neural and associative properties of the human brain, is called subsymbolic.

An operation that is mathematically associative, by definition requires no notational associativity (e.g. addition has the associative property, therefore it does not have to be either left associative or right associative).

Given any expression involving complex numbers, bras, kets, inner products, outer products, and/or linear operators (but not addition), written in bra-ket notation, the parenthetical groupings do not matter (i.e., the associative property holds).

The associative property of an expression containing two or more occurrences of the same operator states that the order operations are performed in does not affect the final result, as long as the order of terms doesn't change.

A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetics operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).