Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: ? 533 Proof
Posted:
Aug 4, 2014 11:33 AM


mueckenh@rz.fhaugsburg.de writes:
> On Sunday, 3 August 2014 23:48:21 UTC+2, Zeit Geist wrote: > >> You have Shown this For Sets of All Finite Cardinalities. >> You have Not Shown that this is True of N itself. > > Nobody can show anything for N itself. All proofs in set theory apply > all natural numbers only.
No, that is a distinction you've made up to get the results you want. In set theory, properties can be proved about N itself. For example whether it is or is not equal to some other set:
{1,2,3} =/= N { n c N  n > 3 \/ n < 4 } = N image(f) = N where f(x) = x
You reject this (you've said that WMaths can't prove properties of such sets) but at the same time you assert the functions like f(x) = x + 1 (from Z to Z) and g(x) = x^3 (from R to R) are bijections. This is why you must never show how you prove that these functions are, indeed, bijections. (Well, at least until you can redefine "bijection" so as to avoid having to show that no elements are missing from the image.)
In set theory, any of the often cited enumerations of Q+ have the provable property that image(e) = Q+ and domain(e) = N.
<snip>  Ben.



