[seqfan] 0^n in general (and in A097135)
Robert Munafo
mrob27 at gmail.com
Sun Jan 24 01:17:25 CET 2010
Wolfram's Mathworld says that 0^0 is indeterminate and quotes Knuth's
mention that 0^0=1 can be useful. (See
http://mathworld.wolfram.com/Power.html or
http://mathworld.wolfram.com/ExponentLaws.html). Eric Weissstein (CRC, 1998)
mentioned it in the "Exponent Laws" heading but without the Knuth reference.
A far better treatment is given in Wikipedia, in the extensive section
http://en.wikipedia.org/wiki/Exponentiation#Zero_to_the_zero_power
They show that you can define it to any value between 0 and 1 by choosing a
suitable path when taking the limit (there are many that result in a value
of 1, far fewer for other limit values). They give several reasons for
0^0=1. The most practical reasons have to do with the Binomial Theorem and
several other similar identities, which otherwise have to be given extra
boundary cases.
It also lists the behaviour of Mathematica and many other computer
computation systems/environments, classified by how they handle 0^0. 0^0=1
is predominant.
On Sat, Jan 23, 2010 at 18:59, Alonso Del Arte <alonso.delarte at gmail.com>wrote:
> I was unaware of A7, and I'm not
> sure I agree with its definition. However, my assertion that 0^0 is
> indeterminate comes not from any deep mathematical understanding on my
> part,
> but was simply my repeating what Mathematica told me.
>
--
Robert Munafo -- mrob.com
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