Sure.  An interesting, if not terribly relevant, fact is that there are more irrational numbers that we *can't* represent the above way than that we can (IIRC).

However, those aren't actually interesting in solving the kinds of problems we want to solve with a programming language, so it's academic, and symbolic representation certainly gains you some things and costs you some things in meaningful engineering kinds of ways.


On Sat, Sep 21, 2013 at 9:41 AM, Brandon Allbery <allbery.b@gmail.com> wrote:
On Sat, Sep 21, 2013 at 12:35 PM, Bardur Arantsson <spam@scientician.net> wrote:
On 2013-09-20 18:31, Brandon Allbery wrote:
[--snip--]
> unless you have a very clever representation that can store
> in terms of some operation like sin(x) or ln(x).)

I may just be hallucinating, but I think this is called "describable
numbers", i.e. numbers which can described by some (finite) formula.

Not sure how useful they would be in practice, though :).

I was actually reaching toward a more symbolic representation, like what Mathematica uses.

--
brandon s allbery kf8nh                               sine nomine associates
allbery.b@gmail.com                                  ballbery@sinenomine.net
unix, openafs, kerberos, infrastructure, xmonad        http://sinenomine.net

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