Re: The reality of sets, on a scale of 1 to 10 [Was: The non-existence of "dark numbers"]

Moebius <invalid@example.invalid> wrote:

Am 24.03.2025 um 21:28 schrieb Alan Mackenzie:

WM <wolfgang.mueckenheim@tha.de> wrote:

On 22.03.2025 15:04, Alan Mackenzie wrote:

WM <wolfgang.mueckenheim@tha.de> wrote:

Tell me, which of these infinite sets is bigger: {0, 4, 8, 12, 16, ....}
and {1, 3, 5, 7, 9, ....}?

The second, of course.

Prove it.

You need only consider finite sections and take the limit. [...]

What on Earth do you mean by "finite sections", if anything?  And take
what limit? [...]

Guess he's referring to this notion:
https://en.wikipedia.org/wiki/Natural_density

OK, thanks.  That natural density is not a property of sets, it's a
property of the natural numbers with additional (arithmetic) structure
applied to them.  The Wikipedia article describes it as a branch of
number theory, not set theory.

--
Alan Mackenzie (Nuremberg, Germany).