Definition:Ordering/Size

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