## digitalmars.D - About 0^^0

- Bill Baxter <wbaxter gmail.com> Dec 09 2009
- Janzert <janzert janzert.com> Dec 09 2009
- Don <nospam nospam.com> Dec 10 2009

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

Dec 09 2009

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

Dec 09 2009

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.

Dec 10 2009