Virgil
Posts:
9,012
Registered:
1/6/11


Re: Matheology � 222 Back to the roots
Posted:
Feb 20, 2013 3:13 PM


In article <374eee06b5b54399b1ab472a93953fec@f6g2000yqm.googlegroups.com>, WM <mueckenh@rz.fhaugsburg.de> wrote:
> On 19 Feb., 23:28, fom <fomJ...@nyms.net> wrote: > > 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.fhaugsburg.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. > > > > Humor us. > > > > Show us for surd(5). > > > > The proof for surd(2) is special because it uses odds and evens. > > And you think that the fundamental theorem of number theory makes a > difference between prime factor 2 and others, say 3 or 5 or 7? Does WM claim that anything proof valid for 2 must also be valid for 3 or 5 or other primes? How about the proof that 2 is even, does that proof make all primes even? 

