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Topic: Why do we need those real non-constructible numbers?
Replies: 68   Last Post: Dec 11, 2017 1:42 AM

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 Jan Burse Posts: 1,472 Registered: 4/12/05
Re: Why do we need those real non-constructible numbers?
Posted: Nov 8, 2017 8:29 AM

The transcendental numbers are uncountable.
Anyway nice trivial lemmas here:

if S' subset S and S countable, then S' countable
if S subset S' and S uncountable, then S' uncountable
https://www.math.brown.edu/~res/MFS/handout8.pdf

Just contraposition, use C(.) for countable:

S' subset S & C(S) -> C(S')

<=>

S' subset S -> (C(S) -> C(S'))

Use other variables:

S subset S' -> (C(S') -> C(S))

Use comntraposition:

S subset S' -> (~C(S) -> ~C(S'))

<=>

S subset S' & ~C(S) -> ~C(S')

So if we could prove the transcendental numbers
uncountable, we would have proved the real numbers
uncountable. Since T subset R.

Anybody up for a direct proof?

bassam king karzeddin schrieb:
>
> Why do we really need those real non-constructible numbers, if it is impossible to express them exactly except only by constructible numbers or as meaningless notation in mind only?
>
> And this intuitive and so simple question not necessarily directed to those described as professional mathematicians since we know exactly how are those captured by so many meaningless definitions that make it impossible for them to think outside their so tinny box or far behind their long noses
>
> But this Q is directed mainly to those amateurs in many fields as mathematics, logic, philosophy, Engineering, independent thinkers, ... etc, as it is very easy for them to recognize reality from fictions since they are quite lucky not to be so much mind pulleted by so many mathematical decisions or non-sensible definitions that are inherited and were imposed on the mathematician's shoulders as absolute facts
>
> People hiding their true identities by using many fictional and masked names are not at all encouraged or welcomed to comment or participate in this important topic since we know in advance their well-exposed and so ill behaviours and intentions for their own purposes, and truly they have nothing to add or nothing to lose when they usually do participate so foolishly just to protect their own products that are full of pure global ignorance
>
> Regards
> Bassam King Karzeddin
> Nov. 6th, 2017
>

Date Subject Author
11/6/17 bassam king karzeddin
11/6/17 wolfgang.mueckenheim@hs-augsburg.de
11/8/17 bassam king karzeddin
11/8/17 wolfgang.mueckenheim@hs-augsburg.de
11/8/17 bursejan@gmail.com
11/8/17 bursejan@gmail.com
11/8/17 wolfgang.mueckenheim@hs-augsburg.de
11/8/17 bursejan@gmail.com
11/8/17 bursejan@gmail.com
11/9/17 bassam king karzeddin
11/9/17 zelos.malum@gmail.com
11/9/17 bassam king karzeddin
11/9/17 bassam king karzeddin
11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/9/17 bassam king karzeddin
11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/13/17 bassam king karzeddin
11/14/17 wolfgang.mueckenheim@hs-augsburg.de
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11/6/17 Stephen G. Giannoni
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11/7/17 bassam king karzeddin
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11/8/17 bassam king karzeddin
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11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/8/17 Jan Burse
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11/8/17 Dan Christensen
11/8/17 wolfgang.mueckenheim@hs-augsburg.de
11/8/17 bursejan@gmail.com
11/8/17 bursejan@gmail.com
11/8/17 Jan Burse
11/8/17 Jan Burse
11/11/17 bassam king karzeddin
11/11/17 zelos.malum@gmail.com
11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/9/17 Tucsondrew@me.com
11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/8/17 Dan Christensen
11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/9/17 Tucsondrew@me.com
11/9/17 Dan Christensen
11/9/17 wolfgang.mueckenheim@hs-augsburg.de
11/9/17 Dan Christensen
11/10/17 wolfgang.mueckenheim@hs-augsburg.de
11/10/17 Dan Christensen
11/11/17 wolfgang.mueckenheim@hs-augsburg.de
11/11/17 zelos.malum@gmail.com
11/11/17 wolfgang.mueckenheim@hs-augsburg.de
11/8/17 Peter Percival
11/11/17 bassam king karzeddin
11/11/17 zelos.malum@gmail.com
11/15/17 bassam king karzeddin
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11/15/17 zelos.malum@gmail.com
11/27/17 bassam king karzeddin
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12/1/17 zelos.malum@gmail.com
12/2/17 bassam king karzeddin
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12/6/17 bassam king karzeddin
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