```Date: Jun 17, 2013 6:36 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 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.My debate with you does not depend on this being possible, however.-- Alan Smaill
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