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: