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.
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