On 21 Mrz., 20:14, fom <fomJ...@nyms.net> wrote: > On 3/21/2013 8:11 AM, WM wrote: > > > > > But I am not interested in the set itself. Not at all! My claim is > > that every member of the set of lines can be removed such that no > > member remains, but every natural number is contained in the list. > > It would be difficult to find WM making > a better statement of his presumption of > completed infinities. > > One has the empty list. > > One has every natural number. > > WM confuses "natural number" with "representation > of natural number" and his intentions to make > such representations. >
That is nonsense. If the natural number is different from the set of its representations, then one can never have, know, or use it. Then one has always to talk about representations of natural numbers. But that is silly. Therefore I have written the natural number one here and here 1. If you are of different opinion, that need not be wrong but irrelevant for the present discussion concerning a list all lines of whcih can be removed without removing the union of these lines. It somewhat resembles the Binary Tree all finite paths of which can be removed without removing the Binary Tree itself.
The reason for all this nonsense is the assumption that the union of finite elements could become actually infinite, could *reach* infinity!