Dan Christensen <Dan_Christensen@sympatico.ca> wrote in news:firstname.lastname@example.org:
> To follow-up on my previous postings at sci.math
...because you think garbage will evolve into real mathematics if you just keep repeating it...?
Your assertion is that 0^0 can be defined to be any value and yet have all the usual rules of exponents apply. You've been given examples that show this is a false statement and have declined to respond to those examples. Rather, you just re-garbage the group.
Note that each of your "theorems" about the rules of exponents specifically exclude using 0 as a base. Using "logic" like this, you could define 3^2 to be anything and just word your theorems "If a is not 3, then these rules work."
So you're asserting that 0^0 can be defined any way one wants, and it won't matter, _provided that one doesn't actually look at 0^0. How utterly insane is that. Guess what? I have developed a new technique whereby I cut off your feet and yet you can still walk as normal, provided you don't try to walk.
This reminds me of something....oh yeah....At a former employer, the faculty had not had raises for a number of years. The oatmeal-brained provost announced with great joy one day that she had come up with a brilliant scheme for getting us all 3% raises. It would be paid for by cutting Summer pay enough to cover the costs. Since many of the faculty were NOT completely crazy, we protested and the conversation got quite heated. It ended with her screaming, "ALL YOU HAVE TO DO TO GET A RAISE IS NOT TEACH IN THE SUMMER!!!" I mean, sheesh! She'd gone to all that hard work of committing Daylight Saving Time to our salaries and we were so ungrateful. (It was suggested that she double her own monthly salary but only work 3 months and then report back to us on how she was enjoying her raise. Response: "Faculty is faculty and administration is administration!" Ah, that tautology clears that up, thanks.)
It doesn't matter how loudly you scream it, it's still crazy to say "ALL YOU HAVE TO DO TO DEFINE 0^0 = 7 IS NEVER TO WRITE 0^0!!!", which is exactly what you're saying when all your theorems begin with "if a is not 0".