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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: 2,701
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 8:41 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 19/06/2013 8:20 AM, Alan Smaill wrote:
> Nam Nguyen <namducnguyen@shaw.ca> writes:
>

>> 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,
>>> please explain why.

>>
>> 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_ ?

>
> I am specifically *not* claiming that I can persuade you that
> some specific structure has property (c). It is enough
> that you admit that (c) is possible.


Sure. As I've stated it's 1 out of 4 possibilities: so (c) is
a possibility.

>
>> 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?

>
> Since you admit (c) is possible, let's consider that case.


Sure.

- In this of (c) you can _verify_ that 0, s(0), s(s(0)) are
finite individuals, in your constructed set named "U".

- In this of (c) you can _NOT verify_ x is a finite individual
given x is in your constructed set named "U".

Agree? If not, please refute my above by clearly _constructing a set_
named "U", per the possibility (c), _without_ your '...' symbol.

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

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


Date Subject Author
6/16/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill
6/16/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Peter Percival
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Peter Percival
6/16/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/18/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Peter Percival
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill
6/17/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/18/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Peter Percival
6/19/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill
6/19/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/19/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/19/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Peter Percival
6/19/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill
6/19/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/19/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/20/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Peter Percival
6/20/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill
6/20/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/21/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
namducnguyen
6/21/13
Read Re: Fundamental Theorem of Calculus: derivative is inverse to integral #7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept
Alan Smaill

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