On 2/19/2013 9:16 AM, WM wrote: > 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.
Show us for surd(5).
The proof for surd(2) is special because it uses odds and evens.