# 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:

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