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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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 Peter Percival Posts: 2,623 Registered: 10/25/10
Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept

Posted: Jun 17, 2013 1:28 AM

Nam Nguyen wrote:
> 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.
>
>

It is not a mystery. The set of natural numbers is the intersection of
all those sets U such that:
(1) (0 e U)
(2) (x e U) => (s(x) e U).

--
I think I am an Elephant,
Behind another Elephant
Behind /another/ Elephant who isn't really there....
A.A. Milne

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