In article <email@example.com>, firstname.lastname@example.org wrote:
> On Saturday, 12 October 2013 20:12:20 UTC+2, Ben Bacarisse wrote: > > > | The principle says that in a set of finite lines, there is always one > | line containing all elements of the set. Simple as that. > | And that priciple does not fail for infinite numbers of lines, because > | every line has a finite number of elements. > > (context the "lines" are sets -- elements in a sequence with Sn+1 > Sn.) > > > It does not seem to be widely accepted as you thought. > > There is nothing "to accept". By construction of the sequence it is > impossible that of two or more finite lines, two or more finite lines contain > more than one of them.
Sufficiently more that 2lines, namely infinitely many, will contain far more than any one line. > > > >> In mathematics this principle never fails. It is too obvious. > > You just said it failed. You said "There is no such beast like all > > elements of the set". If that is the case, how can there be "one line > > containing all the elements of the set"? The principle says there is > > *always* such a line. > > Please read more carefully. There is always a line that contains all elements > that are contained in its predecessors. There is never a line that contains > aleph_0 elements.
But EVERY column does! > > > > In mathematics actually infinite sets simply do not exist.
In WM's wild weird world of WMytheology actually infinite sets simply may not exist, but they do outside of it. >
> > I told you already long ago that in my book "set" is used for potetntially > infinite sets.
Then it is bad mathematics. > > >> If there was an aleph_0, then it must be either in one line of the matrix > >> or in two or more lines. But it cannot be there.
It is already there as any one column of this matrix: 1 2 1 3 2 1 . . .
or any one diagonal of this matrix: 1 1 2 1 2 3 . . .
or even as a row of this matrix: 1 2 3 ... 1 2 ... 1 ... ...
> > > That's how you used it in your definitive, absolutely irrefutable, "proof", > > of something no one but you has every claimed. > > You claimed the existence of aleph_0 natural numbers in the matrix with > exclusively finite lines.
Only if there are also an actually nfinite number of rows.
It there is a last row and last column, there is only space for a finite number of positions.
To get an actually infinite number of positions one must have at least an actually infinite number of rows or an actually infinite number of columns.
But in WM's world, where there are no actually infinite anythings, his diagram is a lie from the start, as it cannot exist in his world.