The wikipedia article on exponentiation https://en.wikipedia.org/wiki/Exponentiation#Zero_exponent
is polluted by warnings against setting (0^0)=1. I have had a very long discussion on the talk page https://en.wikipedia.org/wiki/Talk:Exponentiation You may consider offering support to the point of view that (0^0)=1 Thanks. Bo. Den 10:10 fredag den 28. marts 2014 skrev Marc Simpson <m...@0branch.com>: Simplified: > > (!+/~)i.11 > > >On Fri, Mar 28, 2014 at 9:06 AM, Pascal Jasmin <godspiral2...@yahoo.ca> wrote: >> well done, >> >> the tacit version: >> >> (] !"1 +/~) i.11 >> >> >> >> ----- Original Message ----- >> From: Bo Jacoby <bojac...@yahoo.dk> >> To: "programm...@jsoftware.com" <programm...@jsoftware.com> >> Cc: >> Sent: Friday, March 28, 2014 3:23:06 AM >> Subject: Re: [Jprogramming] Applied APL - How to think like an APL >> programmer? >> >> "his table on page 105 looks interesting. I wonder what is the shortest J >> expression that can reproduce it" >> >> This one may not be the shortest, but it works: >> >> n!"1 n+/n=.i.11 >> >> >> >> >> >> >> Den 0:07 fredag den 28. marts 2014 skrev Jose Mario Quintana >> <jose.mario.quint...@gmail.com>: >> >> Was Wallis himself the first to assume x^0 =1 even for x=0? See, >>> >>> >>> >>>http://www.maths.tcd.ie/pub/HistMath/People/Wallis/RouseBall/RB_Wallis.html >>> >>> >>> >>>Perhaps a Latin fluent member of the forum could shed some light into the >>>dark: >>> >>> >>> >>>https://archive.org/details/ArithmeticaInfinitorum ? >>> >>> >>> >>>At any rate, his table on page 105 looks interesting. I wonder what is the >>>shortest J expression that can reproduce it... :) >>> >>> >>> >>> >>> >>> >>>On Fri, Jan 17, 2014 at 4:22 PM, Roger Hui <rogerhui.can...@gmail.com>wrote: >>> >>>> Come to think of it, the insight that 1=0^0 is required for the standard >>>> statement of polynomials may have come from Ken Iverson. Knuth doesn't >>>> mention this point and only mentions the binomial theorem. (Same with "Ask >>>> a Mathematician".) But the polynomial argument is more convincing because >>>> polynomials are ubiquitous. >>>> >>>> >>>> >>>> On Fri, Jan 17, 2014 at 12:56 PM, Roger Hui <rogerhui.can...@gmail.com >>>> >wrote: >>>> >>>> > Found it. It is in the very same paper. >>>> > http://arxiv.org/PS_cache/math/pdf/9205/9205211v1.pdf . >>>> > >>>> > On page 6, Knuth wrote: >>>> > >>>> > ... The debate stopped there, apparently with the conclusion that 0^0 >>>> > should be undefined. >>>> > >>>> > But no, no, ten thousand times no! Anybody who wants the binomial >>>> theorem >>>> > ... to hold for at least one non-negative integer n _must_ before that >>>> 0^0 >>>> > = 1, ... >>>> > >>>> > >>>> > "Ask a Mathematican" >>>> > >>>> > >>>> http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/ >>>> > has an interesting and useful discussion on this issue. In it the >>>> > "Mathematician" wrote: >>>> > >>>> > Zero raised to the zero power is one. Why? Because mathematicians said >>>> > so. No really, it's true. >>>> > >>>> > And then goes on to explain why 1=0^0 is a good idea. >>>> > >>>> > >>>> > >>>> > >>>> > >>>> > >>>> > On Fri, Jan 17, 2014 at 12:30 PM, Roger Hui <rogerhui.can...@gmail.com >>>> >wrote: >>>> > >>>> >> BTW, Knuth did something else which typifies APL thinking. In a note or >>>> >> paper (I can not find it now), he argued strongly that 1=0^0, not >>>> >> undefined, not 0, not anything else. The common conventional statement >>>> of >>>> >> a polynomial, p(x)=sigma(k=0;k<=n) a[k]*x^k, requires that x^0 be 1. >>>> Some >>>> >> writers are aware of this dependency and, being careful, write instead >>>> the >>>> >> ugly p(x)=a[0]+sigma(k=1;k<=n)a[k]*x^k. >>>> >> >>>> >> Attention to edge cases is typical of APL thinking. It's another way to >>>> >> stay in the world of expressions and away from the world of statements. >>>> >> You know: >>>> >> >>>> >> if k=0 then >>>> >> a[0] >>>> >> else >>>> >> a[k]*x^k >>>> >> endif >>>> >> >>>> >> >>>> >> >>>> >> >>>> >> On Wed, Jan 15, 2014 at 6:20 PM, Roger Hui <rogerhui.can...@gmail.com >>>> >wrote: >>>> >> >>>> >>> One aspect: J/APL programmers tend to stay in the nice world of >>>> >>> expressions and avoid the nastier world of statements. This tendency >>>> >>> pushes you towards array thinking and away from scalar thinking. >>>> >>> >>>> >>> For example, if b is a boolean array, and you want 4 where b is 0 and >>>> 17 >>>> >>> where b is 1, write: >>>> >>> >>>> >>> (4*0=b)+(17*1=b) >>>> >>> >>>> >>> And of course the signs of real numbers x are: >>>> >>> >>>> >>> (x>0)-(x<0) >>>> >>> >>>> >>> Even Knuth, an eminent mathematician and computer scientist but not an >>>> >>> APL programmer, knows to <strike>steal</strike> adopt this idea. See: >>>> Knuth, >>>> >>> *Two Notes on Notation*< >>>> http://arxiv.org/PS_cache/math/pdf/9205/9205211v1.pdf>, >>>> >>> 1992-05-01. In the first half of the paper he describes how "Iverson's >>>> >>> convention" can be used to simplify the statement and manipulation of >>>> sums. >>>> >>> >>>> >>> See also: >>>> >>> >>>> >>> http://www.jsoftware.com/papers/perlis77.htm >>>> >>> http://www.jsoftware.com/papers/perlis78.htm >>>> >>> http://www.jsoftware.com/papers/APLQA.htm#Perlis-foreword >>>> >>> >>>> >>> >>>> >>> >>>> >>> >>>> >>> >>>> >>> On Wed, Jan 15, 2014 at 5:32 PM, Joe Bogner <joebog...@gmail.com> >>>> wrote: >>>> >>> >>>> >>>> I went googling for some deeper material on how to think like an APL >>>> >>>> programmer. I have read/skimmed through a good set of the material on >>>> >>>> http://jsoftware.com/papers/ and have skimmed through many of the >>>> >>>> books listed on http://www.jsoftware.com/jwiki/Books. >>>> >>>> >>>> >>>> Are there any specific recommendations, free or for purchase? Or, >>>> >>>> perhaps I should spend more time with the list above. >>>> >>>> >>>> >>>> I found this, The APL Idiom List by Perlis and Rugaber, which looks >>>> >>>> similar to what I'm looking for: >>>> >>>> http://archive.vector.org.uk/resource/yaleidioms.pdf. >>>> >>>> >>>> >>>> The review of this book looks like what I'm after, >>>> >>>> >>>> >>>> >>>> http://www.amazon.com/Handbook-APL-programming-Clark-Wiedmann/dp/0884050262 >>>> >>>> , >>>> >>>> constructing useful programs and going into more depth. >>>> >>>> >>>> >>>> Or something of the style of The Little Schemer, >>>> >>>> http://scottn.us/downloads/The_Little_Schemer.pdf >>>> >>>> >>>> >>>> I searched the forum and had trouble finding a relevant post >>>> >>>> ---------------------------------------------------------------------- >>>> >>>> For information about J forums see >>>> http://www.jsoftware.com/forums.htm > >> >>> >>>> >>>> >>>> >>> >>>> >>> >>>> >> >>>> > >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>>---------------------------------------------------------------------- >>>For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> >>> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >---------------------------------------------------------------------- >For information about J forums see http://www.jsoftware.com/forums.htm > > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
