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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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bassam king karzeddin

Posts: 1,853
Registered: 8/22/16
Re: Why do we need those real non-constructible numbers?
Posted: Nov 8, 2017 5:15 AM
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On Wednesday, November 8, 2017 at 12:25:59 PM UTC+3, Quadibloc wrote:
> On Monday, November 6, 2017 at 12:21:29 AM UTC-7, bassam king karzeddin wrote:
> > 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?

>
> The real number line is a nice, simple thing.
>
> A line consisting only of the rational numbers is more complicated. And because
> squares have diagonals, and circles have both a circumference and a radius, we
> would have to add other numbers to that.
>
> One can use functions like the log and trig functions on rational numbers to
> construct other numbers that are no longer rational.
>
> But that can also be done with other less well-known functions, like the Bessel
> functions or the Gamma function. These were new functions that can be defined
> using things like integrals from the older, simpler functions, but they aren't
> just combinations of them by arithmetic operations.
>
> Mathematicians can come up with new functions, making more numbers
> constructible. So those numbers must have existed all along.
>
> Thus, a construct which refers simply to "all the numbers", which doesn't give
> the appearance of implying that if you take a stick and cut it with a knife, the
> exact length of the result has to be constructible with mathematical operations
> (and why would anyone want to think that?) avoids the situation where new
> numbers pop out of an impenetrable fog...
>
> John Savard


Then it must be an easy task for you to design exactly a cube in our physical reality with any distance length of its side such that the cube represents a sum or a difference of two other cubes with positive distinct integer sides? can you? wonder!

BKK


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
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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
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bursejan@gmail.com
11/6/17
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Stephen G. Giannoni
11/6/17
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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
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jsavard@ecn.ab.ca
11/8/17
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bassam king karzeddin
11/8/17
Read Re: Why do we need those real non-constructible numbers?
Jim Burns
11/9/17
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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
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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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