wren ng thornton wren at freegeek.org
Fri Oct 8 22:56:36 EDT 2010

```On 10/7/10 8:35 AM, Ketil Malde wrote:
> Christian Sternagel<c.sternagel at gmail.com>  writes:
>> recently I was wondering about the two words "order" and "ordering"
>
> I would use "ordering" to mean the relation or function that orders
> (ranks) elements, and I'd use "order" to refer the actual progression.
> So by applying an ordering, you get elements in a particular order.

+1.

Though, as others've said, they're basically synonymous (functions are
data, and data are functions :)

One caveat is: consider the case where be pick a bunch of numbers at
random, one at a time. The "order" of the numbers would be a relation on
which number we picked before another; whereas the "ordering" of the
numbers would still be the underlying order(ing) of the domain we're
picking numbers from. E.g., if I pick [5,3,7,9] then 5 < 3 according to
the order (in which the numbers were picked) but 3 < 5 according to the
ordering (on the natural numbers).

The other big caveat is that we can talk about "the order" of certain
things (first-order logic, higher-order functions,...) and that has
nothing to do with an ordering (of logic, functions,...). Or at least,
nothing directly related to an ordering.

--
Live well,
~wren
```