
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, >>>>> 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". > > "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

