
Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Posted:
Jun 19, 2013 10:11 AM


On 19/06/2013 7:43 AM, Nam Nguyen wrote: > On 19/06/2013 3:02 AM, Alan Smaill wrote: >> Nam Nguyen <namducnguyen@shaw.ca> writes: >> >>> On 17/06/2013 4:36 AM, Alan Smaill wrote: >> >> [on the possibility that some members of the set {0,s(0),s(s(0)),...} >> are not finite] >> >>>> 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): >> >> For purposes of argument, I accept it. >> >> My question to you is: is it possible that the set in question >> contains only finite elements. >> >> Do you accept or reject my statement here. If you reject, >> please explain why. > > As is, with your '...' being syntactically unformalized, then Yes, > the followings are possible: > > (a) U is finite: containing only finite elements. > (b) U is finite: containing also infinite elements. > (c) U is infinite: containing only finite elements. > (d) U is infinite: containing also infinite elements. > > _All_ those are the possibilities. _Which of those 4 possibilities_ > can you _specifically construct that one can verify_ ? > > You might have (c) in mind, but then from the unformalized and > _unverifiable_ notion of (c), how could you _verify_ the existences > of certain predicate and function sets, hence _verify_ as true or > false the truth values of certain formulas?
If you'd like, I certainly would (re)visit the issue of what it'd mean to _verify the constructed existence of an infinite set_ .
But are you with me so far, acknowledging all those 4 possibilities for your '...' construction of U, as you seem to have with your "I accept it"?
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

