I think the days of fruitful debate
about this topic are well past us now.
What this issue needs at this point
is a decision one way or the other.
There are several ways of doing that
according to the general voting policies
at Apache: exercising those procedures
should not be viewed as "blunt instruments"
but rather time-honored methods of obtaining
clarity on what amounts to a perfect bikeshed
issue where the spec provides no clear guidance
one way or the other.
>________________________________
> From: Rob Weir <robw...@apache.org>
>To: dev@openoffice.apache.org
>Sent: Wednesday, February 13, 2013 12:30 PM
>Subject: Re: Calc behavior: result of 0 ^ 0
>
>On Wed, Feb 13, 2013 at 11:56 AM, Joe Schaefer <joe_schae...@yahoo.com> wrote:
>> 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.
>>
>
>I was waiting to see if there were any persuasive arguments in favor
>of breaking backwards compatibility before deciding whether to do
>that. I think things are getting a little clearer now with Norbert's
>contribution to the discussion. But if (as it seems now) that
>"mathematical correctness" does not justify the change, then my
>position would be that we don't break backwards compatibility.
>
>Also, a veto would be a blunt instrument and I'd rather avoid it if
>further discussion leads to a consensus.
>
>-Rob
>
>>
>>
>>
>>
>>>________________________________
>>> 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.
>>>>>
>>>>
>>>>
>>>>
>>>
>>>
>
>
>
