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