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 21.03.2025 19:48, Alan Mackenzie wrote:

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

On 21.03.2025 18:39, Jim Burns wrote:

On 3/21/2025 3:50 AM, WM wrote:

On 20.03.2025 23:25, Jim Burns wrote:

For sets not.having a WM.size,
Bob vanishing isn't a size.change.

Only if reducing isn't reducing.

What you (WM) think is reducing
isn't reducing.

You confuse the clear fact that in the reality of sets vanishing
means reducing with the foolish claim that cardinality was a
meaningful notion.

Learn that even Cantor has accepted that the positive numbers have
more reality than the even positive numbers.

You mean something like positive numbers have a reality score of 5,
and the even positive numbers only have a reality score of 3?

No, The number of positive numbers is |ℕ|. The number of even natural
numbers is |ℕ|/2.

Hahaha!

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

The mathematically correct answer is that they are both the same size
(cardinality) because there is a bijection between them.  You don't
understand this, so I expect you not to answer the question.

It needs really years of brainwashing to honestly believe that addition
of a number or subset leaves the number of elements unchanged.

No, it just takes mathematical education, which you lack.

It leaves the cardinality unchanged because this notion is tantamount
to potential infinity.

You're stuck in the 1880s.

He said that is not in conflict with the identical cardinality of both
sets. And he was right!

I doubt very much Cantor said such rubbish.

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

 He was a mathematician.

And you are not at all educated in this field.

Wrong.

"Coun[t]able" is simply another name for potential infinity.

Not even close.

You are simply unable to follow reasonable ideas.

Your "reasonable ideas" are mathematical falsehoods.  If your studies and
doctorate were in physics, why are you trying (and failing) to get up to
speed in mathematics?  What's in it for you?

Therefore the sentence "What you (WM) think is reducing isn't
reducing" exhibits you as a snooty dilettante who cannot distinguish
between cardinality and reality.

Hah!  He's got to you, has he?

No, that is my judgement on JB.

Uninformed opinion, you mean.  You're not qualified to make judgments on
other people's mathematical capabilities.

Regards, WM

--
Alan Mackenzie (Nuremberg, Germany).