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Topic: Matheology § 222 Back to the roots
Replies: 6   Last Post: Feb 20, 2013 3:13 PM

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mueckenh@rz.fh-augsburg.de

Posts: 16,178
Registered: 1/29/05
Re: Matheology § 222 Back to the roots
Posted: Feb 19, 2013 10:16 AM
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On 19 Feb., 15:09, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 19 Feb., 11:03, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
>
> >> Do you think that the square root of 2 is rational?
>
> > No, but I know that it has no decimal or binary representation.
>
> So, how do you know it's not rational, then?


Because every rational number has a representation in a finite base.

> Is there "no doubt", as you describe the conclusion of an argument
> using induction over the natural numbers?


No there is no induction required but the simple proof by
contradiction.
Assume sqrt2 = m/n with m,n coprime. You can find it in many places of
the internet, for instance in chapter 3 of my Geschichte des
Unendlichen.

Regrads, WM




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