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.