```Date: Jun 21, 2013 6:16 AM
Author: Alan Smaill
Subject: Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept

Nam Nguyen <namducnguyen@shaw.ca> writes:> On 20/06/2013 5:04 AM, Alan Smaill wrote:>> Nam Nguyen <namducnguyen@shaw.ca> writes:...>>> - 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.>>>> The question is irrelevant to my argument.>> It is relevant: you just don't realize it.You are the one claiming *impossibility*.I don't have to prove anything.> As long as you don't> _cast away_ the informal symbol '...' in your constructed U as> I've previously done on stipulations (1) and (2)  [see the below quote]> then your argument would go nowhere, and virtually every question> would be relevant.>> <quote>>> (1) (0 e U) and (s(0) e U) and (s(s(0)) e U)> (2) (x e U) => (s(x) e U).>> </quote>>>> We just *suppose* we are in situation (c).>> But "suppose" does _not_ necessarily grant you the right to> prove a particular statement as true or false.Of course not --I'm not claiming that.>> Is it *possible* that the only elements of U are those that can be>> proved to be in U, using the inductive definition?>> You have changed the subject, the question: your question now no> longer references about "finite elements", i.e. finitely encoded> elements. So let's go back to where we were.Yes, this is an additional question.But why do you refuse to answer?> Is it possible that Alan's constructed U (constructed with his '...')> would contain only finitely encoded individuals, where '...'> would refer to the Generalized Inductive Definition?>> The answer is Yes, it's possible.>> Can we prove that Alan's constructed U (constructed with his '...')> would contain only finitely encoded individuals, where '...' would> refer to Generalized Inductive Definition?>> The answer is No, we can not prove that.Fine, let's go with that.Now what about the question:   Is it *possible* that the only elements of U are those that can be   proved to be in U, using the inductive definition?"-- Alan Smaill
```