• Bill Baxter (8/8) Dec 09 2009 Found this link about 0^^0:
• Janzert (7/15) Dec 09 2009 Wikipedia also has a section discussing this:
• Don (9/20) Dec 10 2009 Yeah. It's driven by pragmatism. Setting 0^^0 = 1 is highly useful,

Bill Baxter <wbaxter gmail.com> writes:

Found this link about 0^^0:
http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

I think this explains pretty well why Wolfram is justified in saying
0^^0 is indeterminate, but a PL like D is perfectly justified in
saying it's 1.

In particular the article asserts: "Consensus has recently been built
around setting the value of 0^0 = 1"

--bb

Janzert <janzert janzert.com> writes:

On 12/9/2009 11:50 AM, Bill Baxter wrote:
 Found this link about 0^^0:
 http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

 I think this explains pretty well why Wolfram is justified in saying
 0^^0 is indeterminate, but a PL like D is perfectly justified in
 saying it's 1.

 In particular the article asserts: "Consensus has recently been built
 around setting the value of 0^0 = 1"

 --bb

Wikipedia also has a section discussing this:
http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power

Of particular interest may be the list of particular languages, programs 
and calculators that treat it each way:

http://en.wikipedia.org/wiki/Exponentiation#Treatment_in_programming_languages.2C_symbolic_algebra_systems.2C_and_calculators

Janzert

Don <nospam nospam.com> writes:

Bill Baxter wrote:
 Found this link about 0^^0:
 http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
 
 I think this explains pretty well why Wolfram is justified in saying
 0^^0 is indeterminate, but a PL like D is perfectly justified in
 saying it's 1.
 
 In particular the article asserts: "Consensus has recently been built
 around setting the value of 0^0 = 1"
 
 --bb

Yeah. It's driven by pragmatism. Setting 0^^0 = 1 is highly useful, 
especially for the binomial theorem (Knuth says "it *has* to be 1"!)
There are a few contexts where setting 0^^0 = 1 is problematic. But 
AFAIK none of them are relevant for int^^int. And pow() already sets 
0.0^^0.0 = 1.0. So the decision has already been made.

Since Mathematica has such an emphasis on symbolic algebra it's not as 
clear for them. But it's still interesting that Mathematica makes x^^0 
== 1, regardless of the value of x, yet makes 0^^0 undefined.