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Topic: Irrefutable proofs that both Dedekind and Cauchy did not produce
any valid construction of the mythical "real" number

Replies: 4   Last Post: Oct 6, 2017 6:29 AM

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Markus Klyver

Posts: 730
Registered: 5/26/17
Re: Irrefutable proofs that both Dedekind and Cauchy did not produce
any valid construction of the mythical "real" number

Posted: Oct 6, 2017 6:29 AM
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Den fredag 6 oktober 2017 kl. 07:35:28 UTC+2 skrev Zelos Malum:
> Den torsdag 5 oktober 2017 kl. 15:48:33 UTC+2 skrev Markus Klyver:
> > Den torsdag 5 oktober 2017 kl. 09:40:23 UTC+2 skrev Zelos Malum:
> > > Den torsdag 5 oktober 2017 kl. 09:33:08 UTC+2 skrev John Gabriel:
> > > >
> > > > Hee, hee. Dipshit. Nothing you say has any relevance. I have proved that my improved definition meets ALL the criteria. Go fuck yourself! You will be seen as the fucking moron that you are.

> > >
> > > that means it is YOUR definition not dedekind definition, ergo they are NOT dedekind cuts and hence your arguement against it is invalid.
> > >
> > > This is the definition of a strawman. You make up your own shit rather than adress the proper point.
> > >
> > > Your shit doesn't meet it because, again, why can I find rational numbers excluded? The definition says it shouldn't exist any excluded.

> >
> > Could you expand on this? Obviously every Dedekind cuts will not contain all the elements in ?.

>
> It depends a bit on how strict one has to be, using the more general notation it is so all is always contained. It is just that in some instances the upper (or lower, depending on which you choose to focus on) will have an infinitum (or supremum) in the given set.


Right, that's what I was confused about. Rudin only uses the lower set in his construction of the real numbers, which isn't a partition of ?. Of course his construction is equivalent anyway.



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