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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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 Peter Percival Posts: 2,623 Registered: 10/25/10
Re: Fundamental Theorem of Calculus: derivative is inverse to integral
#7 textbook 5th ed. : TRUE CALCULUS; without the phony limit concept

Posted: Jun 20, 2013 3:13 AM

Nam Nguyen wrote:
> On 19/06/2013 6:41 PM, Nam Nguyen wrote:
>> 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,

>>>>
>>>> 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".

>
> "In this possibility of (c)" I meant.
>

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

When you write of constructing a set, do you mean defining it? You use
the word construct and its derivatives rather often, but when I asked if
you were a constructivist you denied it. So what do you mean by construct?

--
I think I am an Elephant,
Behind another Elephant
Behind /another/ Elephant who isn't really there....
A.A. Milne

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