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Topic: Why do we need those real non-constructible numbers?
Replies: 59   Last Post: Nov 15, 2017 12:43 PM

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bursejan@gmail.com

Posts: 5,169
Registered: 9/25/16
Re: Why do we need those real non-constructible numbers?
Posted: Nov 8, 2017 8:16 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

If the a_n are rational numbers, they might
come from a finite process,

it can even be the case that the partial
sums, s_n = sum_i=1^n a_n, which will be

then rational numbers again, might converge,
and then there will be a limit n->oo s_n,

which is not necessary a rational number anymore,
it can be a transcendental number,

https://math.stackexchange.com/q/37121/4414
(elementary-set-theory) (cardinals) (transcendental-numbers)
the transcendental numbers are uncountable.

Am Mittwoch, 8. November 2017 14:10:57 UTC+1 schrieb burs...@gmail.com:
> But SUM a_n where a_n is an arbitary infinite sequence
> is not a finite description.
>
> Am Mittwoch, 8. November 2017 13:44:58 UTC+1 schrieb WM:

> > Am Mittwoch, 8. November 2017 12:58:14 UTC+1 schrieb burs...@gmail.com:
> > > Nope, transcendental numbers don't have a finite
> > > description.

> >
> > "SUM 1/2^n!" is a finite description.
> >

> > > They are the rest of all real line
> >
> > > numbers that are not rational numbers or
> > > algebraic irrational numbers, and as such they
> > >
> > > are uncountable.

> >
> > All finite descriptions belong to a countable set. Everything beyond is unmathematical nonsense, delusions of unmathematical minds.
> >
> > Regards, WM




Date Subject Author
11/6/17
Read Why do we need those real non-constructible numbers?
bassam king karzeddin
11/6/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/8/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bursejan@gmail.com
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bursejan@gmail.com
11/8/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bursejan@gmail.com
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bursejan@gmail.com
11/9/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/9/17
Read Re: Why do we need those real non-constructible numbers?
zelos.malum@gmail.com
11/9/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/9/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/9/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/13/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/14/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/14/17
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genmailus@gmail.com
11/14/17
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bursejan@gmail.com
11/14/17
Read Re: Why do we need those real non-constructible numbers?
bursejan@gmail.com
11/6/17
Read Re: Why do we need those real non-constructible numbers?
Stephen G. Giannoni
11/6/17
Read Re: Why do we need those real non-constructible numbers?
zelos.malum@gmail.com
11/7/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/9/17
Read Re: Why do we need those real non-constructible numbers?
zelos.malum@gmail.com
11/8/17
Read Re: Why do we need those real non-constructible numbers?
jsavard@ecn.ab.ca
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Jim Burns
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Jan Burse
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Dan Christensen
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Dan Christensen
11/8/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bursejan@gmail.com
11/8/17
Read Re: Why do we need those real non-constructible numbers?
bursejan@gmail.com
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Jan Burse
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Jan Burse
11/11/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/11/17
Read Re: Why do we need those real non-constructible numbers?
zelos.malum@gmail.com
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/9/17
Read Re: Why do we need those real non-constructible numbers?
Tucsondrew@me.com
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Dan Christensen
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/9/17
Read Re: Why do we need those real non-constructible numbers?
Tucsondrew@me.com
11/9/17
Read Re: Why do we need those real non-constructible numbers?
Dan Christensen
11/9/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/9/17
Read Re: Why do we need those real non-constructible numbers?
Dan Christensen
11/10/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/10/17
Read Re: Why do we need those real non-constructible numbers?
Dan Christensen
11/11/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/11/17
Read Re: Why do we need those real non-constructible numbers?
zelos.malum@gmail.com
11/11/17
Read Re: Why do we need those real non-constructible numbers?
wolfgang.mueckenheim@hs-augsburg.de
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Peter Percival
11/11/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/11/17
Read Re: Why do we need those real non-constructible numbers?
zelos.malum@gmail.com
11/15/17
Read Re: Why do we need those real non-constructible numbers?
bassam king karzeddin
11/15/17
Read Re: Why do we need those real non-constructible numbers?
Dan Christensen
11/15/17
Read Re: Why do we need those real non-constructible numbers?
zelos.malum@gmail.com

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