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Could you please take such discussion elsewhere, it really does not belong
in the beta test group.
Christoph
--
POV-Ray tutorials, IsoWood include,
TransSkin and more: http://www.tu-bs.de/~y0013390/
Last updated 14 Jun. 2002 _____./\/^>_*_<^\/\.______
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> I would like to point out something not usually thought of: What is 1/0? I
> notice that as the denominator approaches zero, the result approaches
> infinity. 1 dividen into millionths results in a million pieces. 1 divided
> into bajillionths results in a bajillion pieces.
> Just because our digital mathematics aren't up to the task doesn't mean
the
> result doesn't exist. The result of dividing 1 by 0 should be infinity.
Since when does the fact that
limit(x->0 +) of 1/x = infinity
imply that
1/0 = infinity
? It doesn't. Limits at a point of a function have absolutely nothing to do
with the value of a function at that point.
Also note that if you're going from the left hand side (negative numbers),
it approaches *negative* infinity. So the limit of 1/x doesn't even exist at
x=0 unless you specify a direction.
anything divided by zero is undefined. Not just because computers can't
handle it, but because it's mathematically considered to be undefined.
- Slime
[ http://www.slimeland.com/ ]
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> The result of dividing 1 by 0 should be infinity.
I don't agree: it could be -infinity too. I think a function for division by
zero that returns 2 solutions is pretty useless.
--
Apache
POV-Ray Cloth experiments: http://geitenkaas.dns2go.com/experiments/
Email: apa### [at] yahoo com
ICQ: 146690431
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What about the square root function? It has two solutions, but only returns
one. The assumption is that only the positive solution is germane. There are
(of course) many pedestrian functions that return more than one solution.
A case can be made for setting division by zero to "infinite"- not a number,
but a state. Graph it and it is clear. But we assume that this is not what we
are after and return an error. In a similar manner, we assume that even powered
roots are positive unless there is some other indication involved.
Cheers!
Chip Shults
My robotics, space and CGI web page - http://home.cfl.rr.com/aichip
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> What about the square root function? It has two solutions, but only
returns
> one.
The definition of the square root of a x is the *positive* number which
squared, gives you x. The fact that it's positive is part of the definition,
not just because we choose to ignore the negative.
- Slime
[ http://www.slimeland.com/ ]
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Slime <slm### [at] slimelandcom> wrote:
> The definition of the square root of a x is the *positive* number which
> squared, gives you x. The fact that it's positive is part of the definition,
> not just because we choose to ignore the negative.
That's the reason why the classical solution for the second order polynomial
--
#macro N(D)#if(D>99)cylinder{M()#local D=div(D,104);M().5,2pigment{rgb M()}}
N(D)#end#end#macro M()<mod(D,13)-6mod(div(D,13)8)-3,10>#end blob{
N(11117333955)N(4254934330)N(3900569407)N(7382340)N(3358)N(970)}// - Warp -
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Floaating point systems using IEEE convention
take care of the problem of infinity:
a special pattern of bits represent the infinity
a number greater than any other floating point value.
It has a sign too.
IEEE compliant floating point library / processor
observe the following rules
infty + x = infty
x / 0 -> infty
etc
and 1/(1+x) = 1 if x==infty
---------------------------
Every elementary programming lectures
talk about numeration, number representation and
the inifinite problem.
Daniel Frerejacque
------------------
dan### [at] acmorg
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Floaating point systems using IEEE convention
take care of the problem of infinity:
a special pattern of bits represent the infinity
a number greater than any other floating point value.
It has a sign too.
IEEE compliant floating point library / processor
observe the following rules
infty + x = infty
x / 0 -> infty
etc
and 1/(1+x) = 1 if x==infty
---------------------------
Every elementary programming lectures
talk about numeration, number representation and
the inifinite problem.
Daniel Frerejacque
------------------
dan### [at] acmorg
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frerejacque <dan### [at] freefr> wrote:
> x / 0 -> infty
Well, that's just plain wrong. In the n/x function there's a discontinuity
at x=0, which makes n/0 undefined (if you approach x->0 from the right,
the limit will be +infinity, while if you approach from the left, it
will be -infinity; it can't be both at x=0; it's a discontinuity and thus
not defined).
> and 1/(1+x) = 1 if x==infty
If 1+infinity = infinity, then 1/(1+infinity) = 1/infinity = 0
--
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -
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These dicussions have always been out of my league, but I'll make a
fool and a nuisance of myself briefly to add that assigning a +/-
to infinity has always seemed to me about as sensible as the
following conversation:
Person 1: "Look straight ahead. What do you see?"
Person 2: "Nothing, sir, I'm blind."
Person 1: "Oh, in that case, just tell me what color it is."
:)
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