# Category:Associativity

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This category contains results about Associativity.

Definitions specific to this category can be found in Definitions/Associativity.

Let $S$ be a set.

Let $\circ : S \times S \to S$ be a binary operation.

Then $\circ$ is **associative** if and only if:

- $\forall x, y, z \in S: \paren {x \circ y} \circ z = x \circ \paren {y \circ z}$

## Subcategories

This category has the following 8 subcategories, out of 8 total.

### A

### E

### G

### I

### M

### U

## Pages in category "Associativity"

The following 45 pages are in this category, out of 45 total.

### A

- Addition of Cuts is Associative
- Anticommutativity of External Direct Product
- Associative and Anticommutative
- Associative Commutative Idempotent Operation is Distributive over Itself
- Associative Idempotent Anticommutative
- Associative Law of Addition
- Associative Law of Multiplication
- Associativity of Group Direct Product
- Associativity of Hadamard Product
- Associativity on Four Elements
- Associativity on Indexing Set

### C

### E

### I

### M

### P

- Pointwise Addition is Associative
- Pointwise Addition on Complex-Valued Functions is Associative
- Pointwise Addition on Integer-Valued Functions is Associative
- Pointwise Addition on Rational-Valued Functions is Associative
- Pointwise Addition on Real-Valued Functions is Associative
- Pointwise Multiplication is Associative
- Pointwise Multiplication on Complex-Valued Functions is Associative
- Pointwise Multiplication on Integer-Valued Functions is Associative
- Pointwise Multiplication on Rational-Valued Functions is Associative
- Pointwise Multiplication on Real-Valued Functions is Associative