On 3/22/2013 4:24 PM, WM wrote: > On 22 Mrz., 21:54, William Hughes <wpihug...@gmail.com> wrote: >> On Mar 22, 7:24 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 22 Mrz., 16:24, William Hughes <wpihug...@gmail.com> wrote: >> >> <snip> >> >> >> >>>> Infinite sets are different from finite sets >>>> but they do not contain anything >>>> "beyond any finite set". >> >>> Of course. >> >> We have now established that there >> are sets that do not contain anything >> "beyond any finite set" but >> are different from finite sets. > > That is potential infinity. > Actually infinite sets, however, contain something beyond any finite > set.
And you have the responsibility to define that something with precision if you claim it to be mathematically relevant.
Logic relies on type distinction. This goes back to the Aristotelian species and genera.
There is nothing "beyond". There is finite and infinite.
These terms, perhaps, are only meaningful relative to a fixed model of set theory. Since they presume a partition of all sets into the species "finite" and "infinite".
That may be a source of contention. But that is not the source of your nonsense.