Bye

In what differs R from Q if both are totally ordered?

there are many totally ordered sets.
Your question presumes that all totally
ordered sets should be the same --- that is stupidity.

No.
I just do not share the bag-model of infinity.
Cantor did see it but did not believe it:
Rational numbers are as countable as are natural numbers.
Cantor's elusion was that real numbers include
irrational numbers and can nonetheless be counted too.
While nobody will object against the idea that the
uncountable amount of points on a continuum obey
an imagined order, it is definitely
impossible to realize such hypothetical order.
Genuine reals would be uncountable.
Mathematics has been mutilated since as to
understand real numbers as if they were rational numbers at a time.

If one did consequently distinguish R from Q,
then every piece of it would consist of an uncountable
amount of fictitious elements.

Each interval in R is an uncountable set.

A set cannot be uncountable if it has been set element by element.
What mathematics understand as real number is a chimera.

So far mathematics is still far from admitting this.

"fictitous" is not a mathematical term.

While G. Cantor was perhaps correctly blamed a charlatan,
Meray published "Cantors" definition of real numbers
a year before Cantor himself. He remained unnoticed,
presumably because he correctly wrote "fictitious" limit.

Well, that's why 1,000,000.00 Mark were paid in 1925

Was that about 2 shillings then?

No. After inflation, a million was a fortune, more than a million Euros.

Cantor's thinking and Hilbert's wording often correspond to the
hollow pathos of the German empire.

Is this Godwin's law?

Read Hilbert yourself.

In order to fully reveal all
nonsense you should even be familiar with the bible.

I'll eschew nonsense, thank you.

You cannot eschew religious matters without loosing G. Cantor
who asked cardinal Franzelin in vain for support for his abstruse
mathematical ideas.

My main topic is IR+. However you ignored what I am claiming.

You have neither defined IR+ (that's not a standard notation)

Mathematicians understand IR+ like IR but restricted to positive values.

The mistakes are more or less related to each other.
However, denial of the categorical difference between Q and R
seems to be a standard ritual in "modern" mathematics.

Schroedinger's kitty seems to indicate that it harms.

Again, you can't help it: that's physics not mathematics.

The cat is just a different metaphor as the donkey for the same unresolved
in mathematics problem.


- A number is a number is a number.

A rose is a rose is a rose.

While roses are countable, there are countable numbers and uncountable
"numbers"
The latter refer to fictitious (ir)real numbers including irrational ones.

- Dedekind: One can split the entity of ALL rational numbers: >, =, or <.
(I argue: The entity of ALL rational numbers is identical with the
reals.)

Liar: you may assert that, but you haven't argued it (even
unsuccessfully).

The entity of ALL rational numbers is something that cannot be quantified.
Therefore it is something quite different from any rational number.

What is IR^+?

See above.

Bye
Salviati:
.... in ultima conclusione, gli attributi di eguale
maggiore e minore non aver luogo ne gl'infiniti,
ma solo nelle quantità terminate.
IR>|>IR+>|>IR


.

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