Re: Is one-to-one mapping valid for comparing infinite-sized sets?

"Klaus Cammin" <netzklaus@xxxxxxxx> schrieb im Newsbeitrag
news:6m03a2Fe1m0jU1@xxxxxxxxxxxxxxxxxxxx
Salviati schrieb:
However, I am convinced his own
answer was unable to resolve the challenge by Buridan's donkey.

I've told you this before: there's is an unbroken chain of theorems and
their proofs, that lead to real numbers.

Assuming that real numbers are an archimedian ordered field,

I am not sure if this assumption is correct.

1. you can prove, that Dedekind cuts
and the LUB property are equivalent.

I do not doubt that because even serious mathematicans object
against the LUB.

2. then you prove, that every bounded sequence converges to its LUB.

I am just cutious: Is pi a LUB?

3. next, you can prove, that interval nesting works, i.e. that you get a
real number from it.

With nested intervals I am catched within the rationals because I will never
arrive at a difference equal to zero for as many steps as you like.

4. and then you can prove, that every decimal expansion is a real number,

It undoubterly is, provided it is represented by an infinite amount of
elements.

and vice versa, that every real number has a decimal expansion.

No objection.

5. further you can prove, that IR is complete, i.e. that the limit of
every
convergent cauchy sequence actually is a real number.

I do not doubt that with the tiny addition that the limit does not belong to
the rational numbers. Didn't Meray correctly write "fictitious limit"?


However, his sentence
"The natural numbers were made by God" shows that he could not offer an
alternative to Cantor

Until today nobody has ever offered something better for IR than the
above.

Really? Were not Euclid, Archimedes, Spinoza, Galilei, Gauss, and many
others correct while Cantor's rejection of all rationality was at least
highly questionable?
The question I see is not whether or not there is a real number zero
but does it share the same properties with the rational number zero?
I am arguing, real numbers are something quite different even if it is
mostly impossible and therefore of course not at all necessary to use it
differently as compared to rationals.

And you and the other cranks

This is an insult because there are actually people who are even more naive
than Cantor who discredit serious criticism.

with their ridiculous philosphical pretexts
won't either - where the latter is, I believe, a clear consequence of the
former.

A pretext is a reason which is pretended to have caused you to do something.
If you insist that your sentence contibuted something worth to understand
than tell me please what you mean by latter and former.

And: if I were Buridan's donkey,
I'd flip a coin, eat one haystack, and the other the next day ...

With the sympathy of a senior I realize that you didn't realize why this
metaphor is extremely valuable as a hint to still lacking understanding of a
peculiarity of real numbers.

Did you ever take into account the possibility that Schroedingers cat is
just a modern version of Buridan's donkey, and quantum computing originates
from it?
Tell me please, who has a quantum computer that works as promised.

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


.

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