# Category:Min Operation

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

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

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

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

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

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

## Pages in category "Min Operation"

The following 18 pages are in this category, out of 18 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
- Min is Half of Sum Less Absolute Difference
- Min Operation Equals an Operand
- Min Operation is Associative
- Min Operation is Commutative
- Min Operation is Idempotent
- Min Operation on Continuous Real Functions is Continuous
- Min Operation on Toset forms Semigroup
- Min Operation Representation on Real Numbers
- Min Operation Yields Infimum of Operands
- Min Operation Yields Infimum of Parameters
- Min Operation Yields Infimum of Parameters/General Case
- Min Semigroup is Commutative
- Min Semigroup is Idempotent
- Min Semigroup on Toset forms Semilattice
- Minimum Rule for Continuous Functions