openoffice-dev mailing list archives

Site index · List index
Message view « Date » · « Thread »
Top « Date » · « Thread »
From Kay Schenk <kay.sch...@gmail.com>
Subject Re: Calc behavior: result of 0 ^ 0
Date Wed, 13 Feb 2013 17:53:44 GMT
On Wed, Feb 13, 2013 at 9:30 AM, Rob Weir <robweir@apache.org> wrote:

> On Wed, Feb 13, 2013 at 11:56 AM, Joe Schaefer <joe_schaefer@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
>

Given this discussion and research I've done on my own, I will veto this
change and would like to see it reverted. Sorry, Pedro!  and thanks you
Norbert and others for this worthy discussion.


>
> >
> >
> >
> >
> >>________________________________
> >> From: Joe Schaefer <joe_schaefer@yahoo.com>
> >>To: "dev@openoffice.apache.org" <dev@openoffice.apache.org>; Pedro
> Giffuni <pfg@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.mldc@gmail.com>
> >>>To: dev@openoffice.apache.org; Pedro Giffuni <pfg@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 2ยข
> >>>
> >>>Regards
> >>>Ricardo
> >>>
> >>>
> >>>2013/2/13 Pedro Giffuni <pfg@apache.org>
> >>>
> >>>> Hello;
> >>>>
> >>>> >
> >>>> > Da: Norbert Thiebaud
> >>>> ...
> >>>> >On Tue, Feb 12, 2013 at 10:09 PM, Rob Weir <rabastus@gmail.com>
> wrote:
> >>>> >> On Feb 12, 2013, at 10:39 PM, Pedro Giffuni <pfg@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.
> >>>>
> >>>
> >>>
> >>>
> >>
> >>
>



-- 
----------------------------------------------------------------------------------------
MzK

"A great deal of talent is lost to the world
      for want of a little courage."
                             -- Sydney Smith

Mime
  • Unnamed multipart/alternative (inline, None, 0 bytes)
View raw message