Thank you Ricardo;
My suggestion would be to leave things as they are and give the matter a rest.
I personally prefer to focus on other (more necessary) developments like
updating python to version 2.7.4 which will be released this weekend.
We have ample time for testing and if there is new information we can
revise the issue before 4.0 is released.
Pedro.
>________________________________
> Da: RGB ES <rgb.m...@gmail.com>
>A: dev@openoffice.apache.org; Pedro Giffuni <p...@apache.org>
>Inviato: Mercoledì 13 Febbraio 2013 10:43
>Oggetto: 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.
>>
>
>
>
