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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 19, 2013 9:43 AM

On 19/06/2013 3:02 AM, Alan Smaill wrote:
> Nam Nguyen <namducnguyen@shaw.ca> writes:
>

>> On 17/06/2013 4:36 AM, Alan Smaill wrote:
>
> [on the possibility that some members of the set {0,s(0),s(s(0)),...}
> are not finite]
>

>>> 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):

>
> For purposes of argument, I accept it.
>
> My question to you is: is it possible that the set in question
> contains only finite elements.
>
> Do you accept or reject my statement here. If you reject,

As is, with your '...' being syntactically unformalized, then Yes,
the followings are possible:

(a) U is finite: containing only finite elements.
(b) U is finite: containing also infinite elements.
(c) U is infinite: containing only finite elements.
(d) U is infinite: containing also infinite elements.

_All_ those are the possibilities. _Which of those 4 possibilities_
can you _specifically construct that one can verify_ ?

You might have (c) in mind, but then from the unformalized and
_unverifiable_ notion of (c), how could you _verify_ the existences
of certain predicate and function sets, hence _verify_ as true or
false the truth values of certain formulas?

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