
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 9:43 AM


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?
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

