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

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. Great
mathematicians have devised this method.

What on Earth do you mean by "finite sections", if anything?  And take
what limit?  Which great mathematician(s) were supposedly involved in
this method.

The mathematically correct answer is that they are both the same size
(cardinality) because there is a bijection between them.

Nonsense. The "bijection" is invalid because there are always infinitely
many elements following after every defined pair.

You are (?deliberately) ignorant of the definition of bijection.
"Following after every defined pair", if it's not meaningless, is only
the empty set.  The bijection between these two sets exists and is
uncontroversial.

I doubt very much Cantor said such rubbish.

You have pronounced your own sentence: Your opinions are rubbish.

You should be ashamed to be so misinformed and nevertheless a bigmouth.

As I've said more than once, I have a degree in maths.  You do not.
Which one of us is more likely to be misinformed about mathematics?

Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).