Re: Cantor was Right!

anzaurres1@xxxxxxxxxxx said:
>
>
> Tony Orlow (aeo6) wrote:
> > anzaurres1@xxxxxxxxxxx said:
> > >
> > > Tony Orlow (aeo6) wrote:
> > > > anzaurres1@xxxxxxxxxxx said:
> > > > >
> > > > > Tony Orlow (aeo6) wrote:
> > > > >
> > > > > > Of course there are more reals than naturals, but reals are
> > > countable
> > > > > too.
> > > > >
> > > > > What do you mean by "countable"? Does your definition involve
> > > listing
> > > > > all real numbers in a sequence?
> > > > >
> > > > > If so - great. Give us this sequence.
> > > > >
> > > > > I know how to produce a sequence of all rational numbers and can
> > > tell
> > > > > you what rational number is in what position.
> > > > >
> > > > > But I will be willing to suggest to you a bet. If you can produce a
> > > > > sequence of all real numbers and tell me in which postion each real
> > > > > number is, I will pay you $1 million. If you can't - you will stop
> > > > > posting to sci.math until you pay me $1 million.
> > > > >
> > > > > Make sure that your definition of real numbers is such that any
> > > Cauchy
> > > > > sequence of real numbers has a real limit.
> > >
> > > > I don't know enough of Cauchy sequences to know exactly what your
> > > conditions
> > > > are
> > >
> > > Then you don't know what a real number is. And if you don't know what
> > > real numbers are, I doubt if you can enumerate what you don't know.
> > >
> > > Go learn some elementary math and come back once you do, child.
> > >
> > > > Smiles,
> > > >
> > > > Tony
> > >
> > >
> > Eat ***, oh obnoxious one. You're probably half my age. I am learning all the
> > time, which is more than I bet you can say.
>
> > Smiles,
>
> Nice smile.
>
> Look. If I came to sci.physics, claiming that I have a refutation of
> the idea that atoms contain nucleii and then admitted that I don't know
> what an atom is, I would be laughed out of sci.physics, wouldn't I?
>
> That's exactly what you are doing at sci.math. The concept of a Cauchy
> sequence is the basis for understanding real numbers. If Cauchy
> sequences didn't have limits, real numbers could very well be countble.
> But because they do - the real numbers are uncountable.
>
> Explain something to me. Judging by your interest in the countability
> of real numbers, you are a fan of mathematics and real numbers. Then
> why have you denied yourself the real pleasure of learning what other
> people, interested in math, have discovered about real numbers? And I
> don't mean anything advanced. Just your basic sophomore calculus.
>
> Why do you have time to post zillions post to sci.math but don't have
> time to learn calculus? Wouldn't learning be more fun?
>
>
I have leanred a lot here, actually. It's a long time since i have been able to
afford to go to school, and now have a good sized family to take care of. The
countability of the reals is something that perhaps I am not understanding. It
seems to depend on there being only finite numbers of digits in each, to be
countable? I am not sure what the criterion is, but I have come up with a nice
enumeration of them that I hope will turn into something useful. That really
hasn't been my main thrust in here. I have been concentrating more on subsets
of the reals defined by invertible functions on the integers, which are exactly
comparable and not equal, even when infinite. My generalization works perfectly
for finite as well as infinite sets of this type. There is also the dimensional
aspects of higher orders of reals, as well as the realtionship between
rationals and naturals.

When I have time I'll research Cauchy sequences. Right now, I am studying
surreal numbers, and doing my own research in developing my Bigulosity theory
fully.

Now, you want to jump on a mention of an enumeration of the reals, and bet a
million dollars and make me promise to go away, and get all snotty and
obnoxious, and you haven't asked a single question yet about it. I guess I can
see what kind of conversationalist you are. I'll keep that in mind.
--
Smiles,

Tony
.

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