Re: Cantor Confusion

mueckenh@xxxxxxxxxxxxxxxxx wrote:

stephen@xxxxxxxxxx schrieb:

mueckenh@xxxxxxxxxxxxxxxxx wrote:

*** T. Winter schrieb:

Do they define sets as allowed to grow? Not in the quote you supply.
There they talk about set valued variables that can grow.

No. X and Y do not grow, they remain "X" and "Y". The set they denote
does grow. The number of EC states may be n. "n" does not grow. The
number denoted by "n" does grow.

What do you mean by the 'the number denoted by "n" does grow'?
Currently the number of EC states is 25. In a month it will be 27.
Does that mean 25 is going to grow into 27? Will 25 no longer exist?
Or will 25 now mean 27? What do you mean by 'the number denoted by "25" does
grow'?

It is only a matter of definition and in principle no reason for
quarrel. But it is amusing to see ho set theorists insist on the
complete and actual existence of the sets of numbers. Of course 25 will
not switch to 27 but the number of states will switch from 25 to 27.
That's all. Only by this notion we can talk of growing sets and
introduce the notion of potential infinity.

So the number denoted by "n" does not grow? You seem to be switching your position.



The idea that 25 is ever going to be anything but 25 is absolutely ridiculous.
The idea that a set ever changes is equally ridiculous.

No. Compare Fraenkel et all. They talk about to look at the universe of
all sets not as a fixed entity but as an entity capable of "growing".
What they understand and how this growing can take place has lead to
many misunderstandings by underinformed mathematicians. But however one
may interpret their sentence. The universe of all sets can change, to
put it cautiously. That is not at all ridiculous.

Regards, WM

Nobody but you has talked about "growing" sets. Sets, like numbers, do not
grow. You, like many other people who do not understand set theory,
think of sets as mutable objects, that change as we perform operations
on them. This is akin to thinking that numbers change when we perform
addition. If I add 3 to 7, neither 3 or 7 changes.

Stephen

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