From: David Masover <ninja@...>
Date: 2010-11-25T08:17:10+09:00
Subject: Re: Ruby 1.8 vs 1.9

On Wednesday, November 24, 2010 01:35:12 pm Josh Cheek wrote:
> On Wed, Nov 24, 2010 at 1:16 PM, Phillip Gawlowski <
> 
> cmdjackryan@googlemail.com> wrote:
> > On Wed, Nov 24, 2010 at 8:02 PM, Josh Cheek <josh.cheek@gmail.com> wrote:
> > > Its wrongness is an interpretation (I would also prefer that it just
> > 
> > break,
> > 
> > > but I can certainly see why some would say it should be infinity). And
> > > it
> > 
> > > doesn't apply only to Ruby:
> > It cannot be infinity. It does, quite literally not compute. There's
> > no room for interpretation, it's a fact of (mathematical) life that
> > something divided by nothing has an undefined result. It doesn't
> > matter if it's 0, 0.0, or -0.0. Undefined is undefined.
> 
> From my Calculus book (goo.gl/D7PoI)
> 
> "by observing from the table of values and the graph of y = 1/x*²* in
> Figure 1, that the values of 1/x*²* can be made arbitrarily large by
> taking x close enough to 0. Thus the values of f(x) do not approach a
> number, so lim_(x->0) 1/x*²* does not exist. To indicate this kind of
> behaviour we use the notation lim_(x->0) 1/x*²* = ∞"

Specifically, the _limit_ is denoted as infinity, which is not a real number.

> Since floats define infinity, regardless of its not being a number, it is
> not "absurd to the extreme" to result in that value when doing floating
> point math.

Ah, but it is, for two reasons:

First, floats represent real numbers. Having exceptions to that, like NaN or 
Infinity, is pointless and confusing -- it would be like making nil an 
integer. And having float math produce something which isn't a float doesn't 
really make sense.

Second, 1/0 is just undefined, not infinity. It's the _limit_ of 1/x as x goes 
to 0 which is infinity. This only has meaning in the context of limits, 
because limits are just describing behavior -- all the limit says is that as x 
gets arbitrarily close to 0, 1/x gets arbitrarily large, but you still can't 
_actually_ divide x by 0.

They didn't teach me that in Calculus, they're teaching me that in proofs.

> > That other languages have the same issue makes matters worse, not
> > better (but at least it is consistent, so there's that).
> 
> The question was "Is there anything in the above which applies only to Ruby
> and not to floating point computation in another other mainstream
> programming language?" the answer isn't "other languages have the same
> issue", it's "no".

I don't know that there's anything in the above that applies only to Ruby. 
However, Ruby does a number of things differently, and arguably better, than 
other languages -- for example, Ruby's integer types transmute into Bignum 
rather than overflowing.