# Definition:Ordering/Size

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## Definition

An ordering can often be considered to be a comparison of the **size** of objects, perhaps in some intuitive sense.

This is particularly applicable in the context of numbers.

Thus the expression $A \preceq B$ can in such contexts be interpreted as:

**$A$ is smaller than $B$****$A$ is less than $B$**

and $B \preceq A$ can similarly be interpreted as:

**$A$ is larger than $B$****$A$ is greater than $B$**

In natural language, such terms are called **comparative adjectives**, or just **comparatives**.

Depending on the nature of the set being ordered, and depending on the nature of the ordering relation, this interpretation of an ordering as a comparison of size may not be intellectually sustainable.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings