On 3/22/2013 4:42 PM, WM wrote: > On 22 Mrz., 22:31, William Hughes <wpihug...@gmail.com> wrote: >> On Mar 22, 10:14 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 22 Mrz., 21:33, William Hughes <wpihug...@gmail.com> wrote: >> >> <snip> >> >>>> this does not mean that one can do something >>>> that does not leave any of the lines of K >>>> and does not change the union of all lines. >> >>> That is clear >> >> So stop claiming your proof >> means you can do something >> that does not leave any of the lines >> of K and does not change the union >> of all the lines. > > My proof is this: IF there is an actually infinite list of FISONs as I > devised it, THEN all lines can be removed without changing the union > of the lines. This proof has been acknowledged by WH. > > Obviously the result is impossible, hence at least one of the premises > has been contradicted. But the ony premises are 1) induction is valid, > 2) infinity is actual. > > Now you can choose what you like. My choice has been fixed. >
What do you mean by "actuality" in choice number 2?
WM's lack of understanding of these issues merely reflects WM's failure to make any effort at understanding these issues.
Infinity enters matheamatics through Cantorian analysis because of Leibniz' law when accurately stated:
> > "What St. Thomas affirms on this point > about angels or intelligences ('that > here every individual is a lowest > species') is true of all substances, > provided one takes the specific > difference in the way that geometers > take it with regard to their figures." > > Leibniz > > > > "If m_1, m_2, ..., m_v, ... is any > countable infinite set of elements > of [the linear point manifold] M of > such a nature that [for closed > intervals given by a positive > distance]: > > lim [m_(v+u), m_v] = 0 for v=oo > > then there is always one and only one > element m of M such that > > lim [m_(v+u), m_v] = 0 for v=oo" > > Cantor to Dedekind >