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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 11:48 PM

On 17/06/2013 4:36 AM, Alan Smaill wrote:
> 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.
>>

>
> You've seen this several timers already.

I've seen "..." in a lot of crank posts too. (And I'm not saying you're
a crank).

>
> My debate with you does not depend on this being possible, however.

I don't know what you're trying to say here.

My statement here is that your constructed set:

U = {0, s(0), s(s(0)), ... }

could be uncountable and could contain elements that aren't finitely
encoded.

Do you accept or refute my statement here. If you refute, please note
that I had a request (above):

>> State it then in the technical language manner, as I did (1) and (2).

--
----------------------------------------------------
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