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