
Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Posted:
Jun 17, 2013 11:48 PM


On 17/06/2013 4:36 AM, Alan Smaill wrote: > Nam Nguyen <namducnguyen@shaw.ca> writes: > >> On 16/06/2013 3:03 PM, Alan Smaill wrote: >>> Nam Nguyen <namducnguyen@shaw.ca> writes: >>> >>>> On 15/06/2013 1:44 AM, Peter Percival wrote: >>>>> Nam Nguyen wrote: >>>>> >>>>>> >>>>>> No the inductive definition says that in your case of "{0, s(0), >>>>>> s(s(0)), ... }" we'd have: >>>>>> >>>>>> (1) (0 e U) and (s(0) e U) and (s(s(0)) e U) >>>>>> (2) (x e U) => (s(x) e U). >>>>>> >>>>>> In stipulation (2) it does _NOT_ say x must necessarily be finite. >>>>> >>>>> That is why you need a third clause that says (or has the effect that) >>>>> the set being defined is the smallest such U. >>>> >>>> First, you should direct your technical "advice" here to Alan: that's >>>> _his_ definition, _his_ defending of something, we're talking about. >>> >>> It's the standard definition, not mine. >>> And this advice is of course correct. >> >> State it then in the technical language manner, as I did (1) and (2). >> Let's postpone discussing anything else until you could do this. >> >> Remember you had "..." > > You've seen this several timers already.
I've seen "..." in a lot of crank posts too. (And I'm not saying you're a crank).
> > My debate with you does not depend on this being possible, however.
I don't know what you're trying to say here.
My statement here is that your constructed set:
U = {0, s(0), s(s(0)), ... }
could be uncountable and could contain elements that aren't finitely encoded.
Do you accept or refute my statement here. If you refute, please note that I had a request (above):
>> State it then in the technical language manner, as I did (1) and (2).
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

