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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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 namducnguyen Posts: 2,777 Registered: 12/13/04
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 12:34 AM

On 16/06/2013 5:55 PM, 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.
>
> Remember you had "..."

After that then of course you'd next show that your final U would
contain _only_ individuals that are finitely encoded.

I don't think that's possible but we'll wait to see how you might
do that, would be my guess.

--
----------------------------------------------------
There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
----------------------------------------------------

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