\begin{definition}[Definition:Ordering/Size]
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 '''[https://en.wikipedia.org/wiki/Comparative 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.
\end{definition}