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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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 Alan Smaill Posts: 984 Registered: 1/29/05
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 10:20 AM

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,

>
> 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.

> 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.

--
Alan Smaill

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