On Tue, 4 Mar 2014 10:14:20 -0800 (PST), John Gabriel <firstname.lastname@example.org> wrote:
>On Tuesday, 4 March 2014 19:42:29 UTC+2, dull...@sprynet.com wrote: > >> >The first 3 terms is how I know the general term. >> What??? That's not a proof. Not even close. > >I didn't call it a proof. I said that it is how I know the general term.
Right. How do you know the general term? The fact that the first three terms are what they are simply doesn't say anything about the next term - saying "the first three terms" in reply to my question about how you know the general term is just silly.
Unless there's some rule in the New Calculus to the effect that any time you think you see a pattern that apparent pattern must be valid. In which case the New Calculus is simply wrong.
> I asked you how you can know the general term in any other way, but so far, you've not said anything.
No, you never asked that. You made a sarcastic remark when I asked how _you_ knew the general term. In any case: How one knows the general term depends on how one defined sin(x). Starting from what you think is the definition, opposite over hypotenuse, see any decent calculus book. It's a long story (if all the details are included).
How I know the general term is irrelevant to the question of how a person finds the derivative of sin in the New Calculus. The method you showed me depends on knowning the general term of the power series. But you've given no clue how you know the power series, other than the first three terms.
>Therefore, I take it you don't know of another way. :-) > >> Look. Here's a simple example. Say R is the set of all rationals r >> with r > 0 and r^2 > 2. Say L is the set of all rationals r with >> r < 0 or r^2 < 2. Then the pair (L, R) is a Dedekind cut. > >Bullshit. L=(-oo,sqrt(2)) and R=[sqrt(2), oo) => (L,R) is a Dedekind cut.
No it's not. This is why I used the word "ignorant" the other day. You feel free to say that Dedekind cuts are all wrong somehow, even though you simply don't know what a Dedekind cut _is_.
> >Now sonny, take a look at L and R. The limit of L is in R. > >> If we're taking Dedekind cuts as our definition of the reals >> then (L,R) _is_ a real number. > >Crap. (L,R) is a union of two sets with an element that is indeterminate except as an approximation, that is, sqrt(2).
Assuming you're talking about the sets I called L and R, no, sqrt(2) is not an element of either set.
>There is nothing "real" about it.
A real number is whatever the _definition_ of "real number" says is a real number. If we're using the Dedkind cut definition, then yes, (L,R) is a real number.
>Sqrt(2) is an incommensurable magnitude, not a number. :-) > >> Read that again. The pair (L,R) _is_ a real number. Literally. > >Read what I wrote again. :-) What you wrote is garbage. > >> Nothing there about limits. > >You're obviously deluded. :-) See above. > >> Nothing there about some number that trapped between L and R. If there _were_ something in the definition about a number trapped between L and R then you'd be perfectly justiified in being skeptical about why we should believe such a number exiists. > >But of course I am perfectly justified. :-) There is no number trapped between L and R.
Supposing that were true, so what? Nobody said there was.
There's nothing there to refute! _Arguments_ are subject to refutation - you don't give any arguments there, just assertions.
>It is the nightmare of all your mathematics professors and educators who thought they knew... except they really don't know much at all. :-) > >> But there's no such mystery involved. (L, R) is a real number. > >There sure is a mystery to any logical mind. (L, R) is anti-mathematical hogwash. > >> Period. > >Says who? :-)