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.
>>
>
>
>
