# Category:Smallest Elements

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This category contains results about **Smallest Elements**.

Definitions specific to this category can be found in Definitions/Smallest Elements.

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

An element $x \in S$ is **the smallest element** if and only if:

- $\forall y \in S: x \preceq y$

That is, $x$ **strictly precedes, or is equal to,** every element of $S$.

The Smallest Element is Unique, so calling it ** the smallest element** is justified.

The **smallest element** of $S$ is denoted $\min S$.

For an element to be the **smallest element**, all $y \in S$ must be comparable with $x$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

### E

### S

- Smallest Element is Unique (3 P)

## Pages in category "Smallest Elements"

The following 13 pages are in this category, out of 13 total.