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

On 24.03.2025 21:28, Alan Mackenzie wrote:

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.

For every large enough interval [0, n] the quotient of number of elements is about 2. In the limit 2 is attained.

 

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?

Have you never done simple mathematics?

And take
what limit?  Which great mathematician(s) were supposedly involved in
this method.

Try to get better. I will no longer respond to such stupid questions.

 

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.

Try to define a pair that is only followed by the empty set!

The bijection between these two sets exists and is
uncontroversial.

among imbeciles.

As I've said more than once, I have a degree in maths.

But you can't understand the simplest problems like that above.

You do not.

Wrong.

Which one of us is more likely to be misinformed about mathematics?

You show that you can't understand such simple things as the relative magnitudes of the above sets.
Regards, WM