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Topic: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Replies: 38   Last Post: Jun 21, 2013 6:16 AM

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 Alan Smaill Posts: 1,103 Registered: 1/29/05
Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Posted: Jun 16, 2013 5:03 PM

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.

--
Alan Smaill

Date Subject Author
6/16/13 Alan Smaill
6/16/13 namducnguyen
6/17/13 namducnguyen
6/17/13 namducnguyen
6/17/13 Peter Percival
6/17/13 Peter Percival
6/16/13 Alan Smaill
6/17/13 Alan Smaill
6/17/13 namducnguyen
6/18/13 Peter Percival
6/17/13 Alan Smaill
6/17/13 namducnguyen
6/18/13 Peter Percival
6/19/13 Alan Smaill
6/19/13 namducnguyen
6/19/13 namducnguyen
6/19/13 Peter Percival
6/19/13 Alan Smaill
6/19/13 namducnguyen
6/19/13 namducnguyen
6/20/13 Peter Percival
6/20/13 Alan Smaill
6/20/13 namducnguyen
6/21/13 namducnguyen
6/21/13 Alan Smaill