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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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jsavard@ecn.ab.ca

Posts: 403
Registered: 12/12/04
Re: Why do we need those real non-constructible numbers?
Posted: Nov 8, 2017 4:25 AM
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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


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
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
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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
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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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