On Tuesday, March 4, 2014 7:14:20 PM UTC+1, John Gabriel 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. I asked you how you can know the general term in any other way, but so far, you've not said anything. 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. > > > > 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). There is nothing "real" about it. 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. It is the delusional thinking of mediocre mathematicians called Dedekind and Cauchy. :-) > > > > Try as hard as you like, you have not been able to refute anything at the following link: > > > > http://www.spacetimeandtheuniverse.com/math/4507-0-999-equal-one-317.html#post21409 > > > > 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? :-)
Can you show that sin(x) = sin(x) from the first term of the Taylor polynom? From the second? From the third? And so on? Who told you that the Taylor polynom for sin(x) is what it is? There are some need of knowing what sin(x) is before you can evaluate the Taylor polynom or for that matter the Taylor series.