Dan Christensen <Dan_Christensen@sympatico.ca> wrote in news:022664b8- email@example.com:
>> So you're not leaving 0^0 undefined after all > > Yes, I am. Get over it, Barty.
>> That's hardly "undefined." Maybe "indeterminate" is what >> you're looking for. > > In practice, it amounts to the say thing: You can't assume that > 0^0 has any particular value -- not 1 or 0 or any other number. > Deal with it, Barty.
It's certainly a trait of people who can't think that they usually communicate by means of tired cliches. "Deal with it" and "get over it" are the equivalent of a preteen rolling his eyes and slamming his bedroom door.
Note that we have another contradiction: Now you say that we CAN'T define 0^0. Before, you said we CAN define it to be anything we please. You need to make up your mind.
Also, "in practice, it amounts to the same thing" is hardly a statement of mathematical rigor. Your big assertion is that you have "rigorously" extended exponentiation to N_0. Now we see that your "rigor" is, in fact, quite sloppy. In practice, 0.999999999999 is equal to one, but rigorously, it's not.
(And other readers, please note: I did NOT type .9 repeating.)