In article <firstname.lastname@example.org>, WM <email@example.com> wrote:
> On 4 Mai, 22:48, Dan <dan.ms.ch...@gmail.com> wrote: > > > You can have a formula for the list , f(a,b) , that gives the b'th > > digit of the a'th number of the list . > > You're saying b must be bounded (no infinite sequences of digits) , > > but a can be infinite (an infinite amount of finite sequences) . > > This is inconsistent . Why should f(a,b) be a valid list but f(b,a) be > > an invalid list? > > A very clear and correct argument! > Of course there cannot be any asymmetry.
But WM keeps demanding such asymetry, were the very possigilty of symmetry proves him wrong!! > > 1 > 2, 1 > 3, 2, 1 > ... > > But we know from mathematics that a strictly incresing sequence cannot > contain its limit and also that all natural numbers are finite.
> Therefore all lines are finite.
WM argues that all lines must be limited to being finite in a situation in which all columns are required to be infinite.
So all one needs is a transposition to make those rows infinite, and infinite rows are indeed possible.
> They are potentially infinite, i.e., > they are all finite
Then you cannot have any of your infinite columns either. But you have claimed to have them!