<email@example.com> wrote in message news:firstname.lastname@example.org... <snip>
> Above you see their widely known formulation of the natural numbers. They > did not think about the problem of inclusion monotony, probably because > they did not imagine the set in the form of my table. > > 1 > 1, 2 > 1, 2, 3 > ...
That is as as wrong as the other one to which I just have replied, in fact equivalent. Note that the diagonal is in 1-to-1 correspondence with the last line, in the finite as in the infinite: plain geometry.
> In mathematics actually infinite sets simply do not exist.
You are wrong, or at least have never managed to show otherwise.
> According to Cantor "set" does exclude potential infinity. Potential > infinity exists only in analysis.
And I'd agree with that, although it literally means that N as standardly intended is not in fact a set. Are we sure that that is what Cantor said? You make me wonder...
>> I can't see how it can include potentially infinite sets, > > But actually infinite sets do not exist in mathematics at all.
You are wrong: in fact, arguably, they may be the only kind of infinite sets that can be consistently conceived.
> 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.
And yet again we rather and immediately see that that is bollocks, just your equivocation on the terms of a perfectly symmetrical construction.
> It is not a mathematical problem, but only a psychological one.