Re: Is continuum completely filled up?

toshiaki wrote:

"David Marcus" <DavidMarcus@xxxxxxxxxxxxxx> wrote in message
news:MPG.201cde3842cfa4c8989bb8@xxxxxxxxxxxx
If you want to ask a question, try making it clear and concise. I can't
really tell what you are asking (or saying). However, I already told you
that the Godel sentence essentially says, "I am not provable", where
"I" refers to the Godel sentence itself. If you want to see how this is
done, the book "Godel, Escher, Bach" contains a good non-technical
explanation.

As it is mentioned in Wikipedia article "Russel paradox", in common
situations, this sort of statements are avoided as nonsence. But situation
is not so different in sets also.

Just because you say so, doesn't make it true.

Grelling-Nelson paradox doesn't state
about itself, but its property.
Please reffer to Wikipedia article "Russel paradox".
There mentioned
several lists as a title of "applied versions". And there are "list of all
lists that do not contain
themselves", at right side.
As for List of articles starting with the letter "L", is this example of
"list of all lists that contain themselves"?
Can list contain itself? Where does itself contained on the list? Listed as
myself? Then contradiction. Is it not the same as that we add diagonal
number to list of all reals? Is it not that after all articles have been
listed, this list would be completed for the first time? contradiction.
If the item "Japan" is contained in the List of articles about Japan, then
this list is not contained in list of all lists that do not contain
themselves? Is it our choice, whether to contain or not some articles? What
is list of all lists that contain themselves on earth? Other examples of"
list of all lists that do not contain themselves" is natural, except "all
lists that do not contain themselves itself".

These are paradoxes in English. None of them are paradoxes in
Mathematics.

--
David Marcus
.

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