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


Re: � 454 Equality and the axioms of natural numbers
Posted:
Mar 21, 2014 4:30 AM


In article <5f910dc2d62245dab0541ea00ddb33d8@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Thursday, 20 March 2014 22:35:55 UTC+1, Dan Christensen wrote: > > > The real numbers can also be constructed from Peano's axioms. > > That was not the question.
But it is an answer to a question WM was very careful not to ask! > > > It should be > > possible to prove than no irrational number is equal to a natural number. > > That was not the question.
But it is an answer to a question WM was very careful not to ask!
> The question was: If the five truncated Peano axioms, not more and not less, > define the natural numbers
But the "truncated"Peano postulates prove nothing. They require definitions of an initial object and a succesor operation before they can be used to prove anything.
> Don't hesitate to ask if there is anything unclear.
It is not clear why WM is unable to escape from his Wolkenmuekenheim and join the real world of mathematics.. 

