I once encountered a book where the author was aware of the 0^0 "issue" but
had to have lots of polynomials in the book. So he wrote, multiple times,
n
p(x) = a<sub>0</sub> + sigma a<sub>i</sub> x<sup>i</sup>
i=1
Yuck.
On Fri, Mar 28, 2014 at 11:50 AM, Linda Alvord <lindaalv...@verizon.net>wrote:
>
> 0^i.4
> 1 0 0 0
> (i.4)^0
> 1 1 1 1
>
> One or Zero? Both could be right some of the time, and both answers can't
> be
> right all of the time. So isn't the question - Which will be the most
> useful most of time and cause the fewest problems most of the time.
>
> When that is not a good choice for you, since it has been chosen, you must
> correct for the choice you don't want.
>
> Providing a sufficient number of examples when the choice is bad could
> conceivably make a difference but is unlikely.
>
> ^/~ i.4
> 1 0 0 0
> 1 1 1 1
> 1 2 4 8
> 1 3 9 27
>
> Linda
>
>
> -----Original Message-----
> From: programming-boun...@forums.jsoftware.com
> [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Raul Miller
> Sent: Friday, March 28, 2014 9:46 AM
> To: Programming forum
> Subject: Re: [Jprogramming] Applied APL - How to think like an APL
> programmer?
>
> Pollution is a good choice of words here.
>
> There's a problem in assuming that = always has the same meaning. There's
> another problem in assuming that textbooks are accurate. These are
> typically not big problems, but they are (from some points of view)
> significant problems (and the scale of these problems reflect underlying
> flaws in both our educational process and how we manage it).
>
> Watch:
> 0 1 2 3 4 5 * 0
> 0 0 0 0 0 0
>
> When we ask about what 0^0 means, we are asking "what is the number which
> (when not multiplied by zero) would give zero as a result if it was
> multiplied by zero". It's a trash question and any answer is going to be
> trash.
>
> Put differently: you cannot expect a computer to do your thinking for you
> (unless you are prepared to wait infinite time for good answers).
>
> That said, 1=0^0 is just as valid as any other answer. Anyone claiming it's
> a wrong answer (or claiming "it's not even wrong") is missing the point.
> It's a completely valid answer.
>
> The problem is that it's not the only valid answer and that just annoys
> some people. But maybe some people deserve to be annoyed by this kind of
> issue?
>
> Thanks,
>
> --
> Raul
>
>
>
> On Fri, Mar 28, 2014 at 7:32 AM, Bo Jacoby <bojac...@yahoo.dk> wrote:
>
> > 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-z
> eroth-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
> >
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
> ----------------------------------------------------------------------
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>
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