[Slightly OT]: More on ints and floats

[L.C.]

I would ask a different question. What exactly would be the BENEFIT 
of doing everything in FP ?

I believe programming usually deals with practical, performance/cost
issues, so discarding that to make a point does make the issue sort 
of academical anyway. 

Integers are more efficient in storage space as they do not have to
store a mantissa. They are also precise, as you mentioned. Floats 
have the bad habit of not fitting properly in our binary formats and
thus propagating errors even within their precision range (try 
representing 0.3 or 0.1).

After all, they make hammers in different sizes for a reason.

--
L.C. (Laurentiu C Badea)

Tim Daneliuk <tundra at tundraware.com> wrote in message news:<fjss6b.1021.ln at boundary.tundraware.com>...
> OK, I don't want to resurrect another interminable discourse in ints,
> floats, and how they are/ought/can be handled in the language. But, I
> have a sort of theoretical mathematical question which the whole
> business brought to mind.
> 
> As I understand it, integers and floats are distinct mathematical
> entities. A colleague of mine claims, that insfar as we use them in
> computing, ints are merely a proper subset of floats. He furthermore
> asserts that (again as regards to computing) the distinction between
> them was made as a purely as a practical matter because floating point
> arithmetic was historically computationally expensive. He argues that
> any place one can use an int, these days (with cheap FP hardware), one
> could use a float 0 extended to the precision of the machine and get
> equivalent computational results. Say the hardware supported 4 digits of
> precision. He is arguing that:
> 
> 
>     3/4.0000  is equivalent to 3.0000/4.0000
> 
> (Never mind the old Python modulo vs. divison debate.)
> 
> In effect he is saying that, unless there is a practical
> performance/cost issue at hand, there is no real reason to
> differentiate between ints and floats in practical programming
> problems.
> 
> As a matter of 'pure' mathematics, I argued that ints and floats are
> very different critters. My argument (which is no doubt formally very
> weak) is that the integer 3 and the float 3.0000 are different because
> of the precision problem.  For instance, the integer 3 exists at a single
> invariant point on the number line, but 3.0000 represents all numbers
> from 2.99995 through 3.00004.
> 
> Could one of the genius mathematicians here bring some clarity to this
> discussion, please?
> 
> TIA,