On Thursday, February 27, 2014 6:54:55 AM UTC-5, muec...@rz.fh-augsburg.de wrote: > On Thursday, 27 February 2014 10:15:41 UTC+1, Virgil wrote: > > > > > > > Any set satisfying the Peano postulates can serve as "the" set of > > > > > > natural numbers. > > > > Not in mathematics. > > > > This sequence satifies the Peano axioms: > > 0, 0.9, 1.8, 2.7, ... > > > > What axiom is violated? >
The axioms only specify the name of the of the first number. (Even for that, we have some leeway -- usually 0 or 1). In theory, you can choose whatever symbols you like for the rest. You could, however, get into trouble in your example if you attach multiple meanings to the same symbol.