On 3/22/2013 2:37 PM, WM wrote: > On 22 Mrz., 16:24, William Hughes <wpihug...@gmail.com> wrote: > >>> And what is in your opinion beyond any finite set of lines? >> >> There is no such thing >> as "beyond every finite set of lines". >> Infinite sets are different from finite sets >> but they do not contain anything >> "beyond any finite set". > > The decimal expansion of pi is not beyond any finite (i.e. rational) > approximation?
Finite approximations are not sets of lines.
It is true that if one is *given* a *particular* finite approximation of pi -- that is, a *fixed* finite approximation -- then one can *calculate* a second *particular* finite approximation which, when compared with the first on the basis of the length of the expression as a concatenation of symbols, is longer than the *given* *particular* finite approximation.
In this way, your remark may be comparable.
Since pi is not equal to either finite approximation, you assume completed infinities in the use of the name.
Similarly, you assume completed infinities in all of your lists. This is clear since you do not honestly intend to make all of the crayon marks needed to support your various claims and since you refuse to define your non-standard use of terms to be meaningful.