# Category:Max Operation

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This category contains results about **Max Operation**.

Definitions specific to this category can be found in Definitions/Max Operation.

Let $\struct {S, \preceq}$ be a totally ordered set.

The **max operation** is the binary operation on $\struct {S, \preceq}$ defined as:

- $\forall x, y \in S: \map \max {x, y} = \begin{cases}

y & : x \preceq y \\ x & : y \preceq x \end{cases}$

## Pages in category "Max Operation"

The following 25 pages are in this category, out of 25 total.

### M

- Mapping on Integers is Endomorphism of Max or Min Operation iff Increasing
- Mapping on Integers is Homomorphism between Max or Min Operation iff Decreasing
- Max is Half of Sum Plus Absolute Difference
- Max of Subfamily of Operands Less or Equal to Max
- Max Operation Equals an Operand
- Max Operation is Associative
- Max Operation is Commutative
- Max Operation is Idempotent
- Max Operation on Continuous Real Functions is Continuous
- Max Operation on Natural Numbers forms Monoid
- Max Operation on Toset forms Semigroup
- Max Operation on Woset is Monoid
- Max Operation Preserves Total Ordering
- Max Operation Representation on Real Numbers
- Max Operation Yields Supremum of Operands
- Max Operation Yields Supremum of Parameters
- Max Operation Yields Supremum of Parameters/General Case
- Max Semigroup is Commutative
- Max Semigroup is Idempotent
- Max Semigroup on Toset forms Semilattice
- Maximum Rule for Continuous Functions