R help - May 2014 - 0^0 computation in R : Why it is defined 1 in R ?

Dear R helpers,


today I found something interesting in R. 0^0 gives value 1 in R. But it
is undefined in mathematics. During debugging a R code, I found it and it
effects my program severely. So my question is why it is defined 1 in R?
Is there any particular reason or its a bug in the R software?

Here is one demo:

*************************************************

ff=function(u){
  return( x^0 * u)
}

x=0
zz=integrate(ff,lower=0,upper=1)$value
zz


> source('~/.active-rstudio-document')
> zz
[1] 0.5
>
*************************************************

Looking forward to hear any response.

Regards,

Ritwik Bhattacharya
Indian Statistical Institute Kolkata

On 26/05/2014 13:16, ritwik_r at isical.ac.in wrote:
> Dear R helpers,
>
>
> today I found something interesting in R. 0^0 gives value 1 in R. But it
> is undefined in mathematics. During debugging a R code, I found it and it
> effects my program severely. So my question is why it is defined 1 in R?
> Is there any particular reason or its a bug in the R software?
Try reading the help:

      Users are sometimes surprised by the value returned, for example
      why ?(-8)^(1/3)? is ?NaN?.  For double inputs, R makes use of IEC
      60559 arithmetic on all platforms, together with the C system
      function ?pow? for the ?^? operator.  The relevant standards
      define the result in many corner cases.  In particular, the result
      in the example above is mandated by the C99 standard.  On many
      Unix-alike systems the command ?man pow? gives details of the
      values in a large number of corner cases.

See ?F9.4.4 of the C99 standard.

>
> Here is one demo:
>
> *************************************************
>
> ff=function(u){
>    return( x^0 * u)
> }
>
> x=0
> zz=integrate(ff,lower=0,upper=1)$value
> zz
>
>
>
>> source('~/.active-rstudio-document')
>> zz
> [1] 0.5
>>
>
> *************************************************
>
> Looking forward to hear any response.
>
> Regards,
>
> Ritwik Bhattacharya
> Indian Statistical Institute Kolkata
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
PLEASE do ....


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

You might find searching the web on this topic educational. Consider [1] and
[2], for example.

I doubt this will be changing, so you should do your exponentiation in a
function that handles your special case.

By the way, as nice as RStudio might be, it is not R... it USES R. Examples like
yours won't run as-is in vanilla R so are not really reproducible for
(probably most) readers of this list. Please (re-)read the Posting Guide.

[1] http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
[2]
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/
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On May 26, 2014 5:16:21 AM PDT, ritwik_r at isical.ac.in
wrote:
>Dear R helpers,
>
>
>today I found something interesting in R. 0^0 gives value 1 in R. But
>it
>is undefined in mathematics. During debugging a R code, I found it and
>it
>effects my program severely. So my question is why it is defined 1 in
>R?
>Is there any particular reason or its a bug in the R software?
>
>Here is one demo:
>
>*************************************************
>
>ff=function(u){
>  return( x^0 * u)
>}
>
>x=0
>zz=integrate(ff,lower=0,upper=1)$value
>zz
>
>
>
>> source('~/.active-rstudio-document')
>> zz
>[1] 0.5
>>
>
>*************************************************
>
>Looking forward to hear any response.
>
>Regards,
>
>Ritwik Bhattacharya
>Indian Statistical Institute Kolkata
>
>______________________________________________
>R-help at r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help
>PLEASE do read the posting guide
>http://www.R-project.org/posting-guide.html
>and provide commented, minimal, self-contained, reproducible code.