OTOH I haven't seen anyone issue a technical
veto on this change, which is really what's
required before Pedro actually needs to revert
anything.
>________________________________
> From: Joe Schaefer <joe_schae...@yahoo.com>
>To: "dev@openoffice.apache.org" <dev@openoffice.apache.org>; Pedro Giffuni
><p...@apache.org>
>Sent: Wednesday, February 13, 2013 10:53 AM
>Subject: Re: Calc behavior: result of 0 ^ 0
>
>
>Honestly I'd say that if anything is clear,
>it's that changing away from the status quo
>currently enjoys zero consensus.
>
>As a Ph.D. mathematician who knows about Bourbaki,
>all I can say is that line of argument is curious
>here. There are no authorities other than the spec
>to turn to about how you want POWER(0,0) to behave-
>as a function of 2 variables returning an error is
>probably best mathematically because the POWER
>function isn't remotely continuous at (0,0), but as
>part of an implementation of power series
>representations of sums involving 0^0, returning 1
>is better.
>
>
>
>In any case, the idea for how issues like this should
>be resolved at Apache is always in favor of stability;
>that's why the impetus for consensus away from the current
>behavior is required, not a general discussion about
>which behavior is better given two equal choices
>in the abstract. A prior decision has already been made
>about the code, and those that wish to change it need
>to demonstrate consensus for the change, not the other
>way around.
>
>
>
>HTH
>
>
>
>
>>________________________________
>> From: RGB ES <rgb.m...@gmail.com>
>>To: dev@openoffice.apache.org; Pedro Giffuni <p...@apache.org>
>>Sent: Wednesday, February 13, 2013 10:43 AM
>>Subject: Re: Calc behavior: result of 0 ^ 0
>>
>>Not answering any particular message, so top posting.
>>
>>Two points:
>>
>>a) Of course you can always redefine a function to "fill holes" on non
>>defined points: for example, redefining sinc(x) = sin(x)/x to be 1 on x=0
>>makes sense because you obtain a continuous function... but that's on 1
>>variable: when you go to two variables things become more difficult. In
>>fact, the limit for x^y with x *and* y tending to zero do NOT exists
>>(choose a different path and you'll get a different limit), then there is
>>NO way to make that function continuous on (0,0), let alone what happens
>>when x < 0... so the real question is: does it make sense to "fill the
>>hole" on x^y? *My* answer (and that leads to the second point) is no
>>because it do not give any added value.
>>
>>b) Considering that we are near to 90 messages on this thread it is quite
>>clear that an agreement is not possible. On this situation it is also clear
>>that
choosing an error instead of a fixed value is the best bet.
>>
>>Just my 2¢
>>
>>Regards
>>Ricardo
>>
>>
>>2013/2/13 Pedro Giffuni <p...@apache.org>
>>
>>> Hello;
>>>
>>> >
>>> > Da: Norbert Thiebaud
>>> ...
>>> >On Tue, Feb 12, 2013 at 10:09 PM, Rob Weir <rabas...@gmail.com> wrote:
>>> >> On Feb 12, 2013, at 10:39 PM, Pedro Giffuni <p...@apache.org> wrote:
>>> >>
>>> >>> (OK, I guess it's better to re-subscribe to the list).
>>> >>>
>>> >>> In reply to Norbert Thiebaud*:
>>> >>>
>>> >>> In the Power rule, which *is* commonly used for differentiation, we
>>> take a series
>>> >>> of
polinomials where n !=0. n is not only different than zero, most
>>> importantly,
>>> >>> it is a constant.
>>> >
>>> >Power Rule : d/dx x^n = n.x^(n-1) for n != 0 indeed.
>>> >so for n=1 (which _is_ different of 0 !)
>>> >d/dx X = 1.x^0
>>> >for _all_ x. including x=0. (last I check f(x) = x is differentiable in 0.
>>> >
>>> >I know math can be challenging... but you don't get to invent
>>> >restriction on the Power Rule just to fit you argument.
>>> >
>>>
>>> I will put it in simple terms. You are saying that you can't calculate the
>>> slope of the equation:
>>>
>>> y =a*x + b
>>>
>>> because in the process you need to calculate the value of x^0.
>>>
>>>
>>> >>>
>>>
>>> >>> In the case of the set theory book, do note that the author is
>>> constructing
>>> >>> his own
algebra,
>>> >
>>> >The fact that you call 'Nicola Bourbaki' 'the author', is in itself
>>> >very telling about your expertise in Math.
>>> >I nicely put a link to the wikipedia page, since laymen are indeed
>>> >unlikely to know 'who' Borbaki is.
>>> >
>>>
>>> Do I really care if the name of the author is fictitious or real?
>>>
>>> >>> that get outside his set: 0^0 and x/0 are such cases. The text is not
>>> >>> a demonstration, it is simply a statement taken out of context.
>>> >
>>> >You ask for a practical spreadsheet example, when one is given you
>>> >invent new 'rules' to ignore' it.
>>>
>>> You haven't provided so far that practical spreadsheet.
>>>
>>> >You claim that 'real mathematician' consider 0^0=... NaN ? Error ?
>>> >And when I gave you the page and line from one of the most rigorous
>>> >mathematical
body of work of the 20th century (yep Bourbaki... look it
>>> >up)
>>> >you and hand-wave, pretending the author did not mean it.. or even
>>> >better " if this author(sic) *is* using mathematics correctly."
>>> >
>>>
>>> The thing is that you are taking statements out of context. I don't
>>> claim being a mathematithian. I took a few courses from the career for
>>> fun.
>>>
>>> In the case of set theory you can define, for your own purposes, a special
>>> algebra where:
>>>
>>> - You redefine your own multiplication operator (x).
>>> - You don't define division.
>>> - You make yor algebra system fit into a set of properties that
>>> is useful for your own properties.
>>>
>>> Once you define your own multiplication (which is not the same
>>> multiplication supported in a spreadsheet) You work around the
>>> issue in the power operator by defining the undefined
case.
>>>
>>> These are all nice mathematical models that don't apply to a spreadsheet.
>>>
>>> >>>
>>> >>> I guess looking hard it may be possible to find an elaborated case
>>> where
>>> >>> someone manages to shoot himself in the foot
>>> >
>>> >Sure, Leonard Euler, who introduced 0^0 = 1 circa 1740, was notorious
>>> >for shooting himself in the foot when doing math...
>>> >
>>> >For those interested in the actual Math... in Math words have meaning
>>> >and that meaning have often context. let me develop a bit the notion
>>> >of 'form' mentioned earlier:
>>> >for instance in the expression 'in an indeterminate form', there is
>>> >'form' and it matter because in the context of determining extension
>>> >by continuity of a function, there are certain case where you can
>>> >transform you equation into another 'form' but
if these transformation
>>> >lead you to an 'indeterminate form', you have to find another
>>> >transformation to continue...
>>> >hence h = f^g with f(x)->0 x->inf and g(x)->0 x->inf then -- once it
>>> >is establish that h actually converge in the operating set, and that
>>> >is another topic altogether -- lim h(x) x->0 = (lim f)^(lim g).
>>> >passing 'to the limit' in each term would yield 0^0 with is a
>>> >indeterminable 'form' (not a value, not a number, not claimed to be
>>> >the result of a calculation of power(0,0), but a 'form' of the
>>> >equation that is indeterminate...) at which point you cannot conclude,
>>> >what the limit is. What a mathematician is to do is to 'trans-form'
>>> >the original h in such a way that it lead him to a path to an actual
>>> >value.
>>> >
>>> >in other words that is a very specific
meaning for a very specific
>>> >subset of mathematics, that does not conflict with defining power(0,0)
>>> >= 1.
>>> >
>>> >
>>> >wrt to the 'context' of the quote I gave earlier:
>>> >
>>> >"Proposition 9: : Let X and Y be two sets, a and b their respective
>>> >cardinals, then the set X{superscript Y} has cardinal a {superscript
>>> >b}. "
>>> >
>>> >( I will use x^y here from now on to note x {superscript y} for
>>> readability )
>>> >
>>> >"Porposition 11: Let a be a cardinal. then a^0 = 1, a^1 = a, 1^a = 1;
>>> >and 0^a = 0 if a != 0
>>> >
>>> >For there exist a unique mapping of 'empty-set' into any given set
>>> >(namely, the mapping whose graph is the empty set); the set of
>>> >mappings of a set consisting of a single element into an arbitrary set
>>> >X is equipotent to X (Chapter II, pragraph 5.3); there
exist a unique
>>> >mapping of an arbitrary set into a set consisting of a single element;
>>> >and finally there is not mapping of a non-empty set into the
>>> >empty-set;
>>> >* Note in particular that 0^0 = 1
>>> >"
>>>
>>> Again, I will stand to what I said: this statement is not a demonstration
>>> and is taken out of context. The definition is given to conform with this
>>> "unique mapping" which unfortunately doesn't exist in the real world.
>>>
>>>
>>> >
>>> >Here is the full context of the quote. And if you think you have a
>>> >proof that there is a mathematical error there, by all means, rush to
>>> >your local university, as surely proving that half-way to the first
>>> >volume, on set theory, of a body of work that is acclaimed for it's
>>> >rigor and aim at grounding the entire field of mathematics soundly in
>>> >the rigor of set
theory, there is an 'error', will surely promptly get
>>> >you a PhD in math... since that has escaped the attentive scrutiny and
>>> >peer review of the entire world of mathematicians for decades...
>>> >
>>>
>>> I lost contact with my teacher, indeed quite an authority, but for some
>>> reason he disliked computer math to the extreme anyways.
>>>
>>> Pedro.
>>>
>>
>>
>>
>
>
