
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 8:41 PM


On 19/06/2013 8:20 AM, Alan Smaill wrote: > Nam Nguyen <namducnguyen@shaw.ca> writes: > >> 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_ ? > > I am specifically *not* claiming that I can persuade you that > some specific structure has property (c). It is enough > that you admit that (c) is possible.
Sure. As I've stated it's 1 out of 4 possibilities: so (c) is a possibility.
> >> 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? > > Since you admit (c) is possible, let's consider that case.
Sure.
 In this of (c) you can _verify_ that 0, s(0), s(s(0)) are finite individuals, in your constructed set named "U".
 In this of (c) you can _NOT verify_ x is a finite individual given x is in your constructed set named "U".
Agree? If not, please refute my above by clearly _constructing a set_ named "U", per the possibility (c), _without_ your '...' symbol.
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

