Mathematics in Python are not correct

[Arnaud Delobelle]

Dan Bishop <danb_83 at yahoo.com> writes:

> On May 8, 6:14 pm, Luis Zarrabeitia <ky... at uh.cu> wrote:
>> On Thursday 08 May 2008 06:54:42 pm wxPytho... at gmail.com wrote:
>>
>> > The problem is that Python parses -123**0 as -(123**0), not as
>> > (-123)**0.
>>
>> Actually, I've always written it as (-123)**0. At least where I'm from,
>> exponentiation takes precedence even over unary "-". (to get a power of -123,
>> you must write $(-123)^0$ [latex])
>
> FWIW, my TI-89 evaluates it as -1.
>
>> Though not an authoritative source, wikipedia also uses the (-x)^y
>> notation:http://en.wikipedia.org/wiki/Exponentiation#Powers_of_minus_one
>>
>> Btw, there seems to be a math problem in python with exponentiation...
>>
>> >>> 0**0
>>
>> 1
>>
>> That 0^0 should be a nan or exception, I guess, but not 1.
>>
>> [just found out while trying the poster's example]
>
> Technically correct, but 0**0 == 1 is actually pretty useful.  For one
> thing, it lets you create a Vandermonde matrix without making 0 a
> special case.

If we want Binomial expansion to work sanely, we need 0^0 = 1, e.g:

(x+0)^2 = 1*x^2*0^0 + 2*x*0 + 1*x^0*0^2
        = x^2

Therefore 0^0 = 1

Also, x^y (for x, y natural numbers) can be defined as the number of
functions from Y to X where |X|=x and |Y|=y.  As there is exactly one
function from the empty set to the empty set, 0^0 = 1.

The arguments for making 0^0 = 0 are weak, it is a bit more convincing
to want it to be undefined (as (0,0) is a point of discontinuity of
(x,y) -> x^y).
-- 
Arnaud