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.
