Re: dpkg doing wrong math (0.09 = 0.9) ?-
On Mon, Aug 21, 2006 at 08:10:46PM +0200, Florian Weimer wrote:
> * Lionel Elie Mamane:
>> Well, I have found one. Myself. You just have to interpret the part
>> after the second point as the integer part of an infinitesimal:
>> Let ε be an infinitesimal, that is a strictly positive number
>> (that is ε > 0) smaller than any strictly positive real number
>> (that is ∀ n ∈ ℕ, n>0 implies ε < 1/n ).
> Such a number does not exist because every set of reals which has a
> lower bound has a real number as its infimum.
I didn't say it is a real number, and indeed no such real number
exists. You need a richer notion of number than real numbers.
> (Of course, such arithmetic structures can be defined, but it's a
> lot more involved than that.)
Precisely. One such structure is John Conway's surreal numbers. (As I
already said in my previous email.)
>> Then the version number x.y.z is interpreted as:
>> x.y + z * ε
>> (And a.b.c.d is interpreted as a.b + c.d * ε)
> In this context, it does not make much sense to allow only
> non-negative integers for z,
You can accept any real for z, yes. I was working the other way round:
give a meaning to x.y.z, where x, y and z are non-negative
integers. The non-negative integers restriction comes from the
problem statement, not from the solution :)
> so your interpretation is anything but natural
As the battles between formalists, intuitionists, platonists,
constructivists, fictionalists, etc show, what is "natural" is highly
subjective. However, if the goal of the game is to construct an
extension to x.y.z of the interpretation of x.y as the decimal
rational number usually written that way, I find my interpretation
quite "natural". If you disagree, good for you. No amount of
discussion is going to make us agree on what is "natural" anyway, as
it is not a well-defined concept.
> and as good as any other total odering.
I'd certainly be less happy with an ordering that gives:
1.2.3 < 1.2.2 < 1.2.5