12 Jul
2010
12 Jul
'10
7:51 p.m.
On Jul 11, 2010, at 9:20 PM, Daniel Fischer wrote:
* Prove the binomial theorem *without* the convention 0**0 := 1
Except that in the binomial theorem, one uses (^) and not (**). For (^), setting x ^ 0 = 1 is, as far as I'm aware, uncontested.
This is not so: the exponent in the binomial theorem is a real number, not an integer. See http://mathworld.wolfram.com/BinomialTheorem.html Real numbers turn up in surprising places. I imagine most of us are familiar with the derivative operator D, and with iterations of it like second derivatives. But it's not just natural number powers of D that make sense; there are fractional derivatives, and D**(1/2) does find uses.