Re: An uncountable countable set
- From: Virgil <vmhjr2@xxxxxxxxxxx>
- Date: Sat, 01 Jul 2006 14:47:11 -0600
In article <1151759780.766369.176910@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:
Virgil schrieb:If you claim that any member of any list is not differentiated from the
Cantor's diagonal proof does not prove that all numbers of the list are
included.
All number of the list are certainly included in the list. What else are
they supposed to be included in???
Cantor's diagonal proof does not prove that all numbers of the list are
included in that sense that all are covered by the diagonal.
number created for that list by any of uncountably many variations of
Cantor's constructions, then you must be declaring there there exists a
first number in some list which is not differentiated according to some
version of Cantor's rules.
So Give us an example of this alleged situation. If you can.
If I declare that there re fairies at the bottom of my garden, such a
declaration will be rejected without solid evidence.
"Mueckenh" declares the equivalent of fairies at the bottom of Cantor's
garden, but cannot produce any evidence of their existence. We will not
take his word for it, and we will not accept the lame argument he has
presented as anything but lame arguments.
Only to
give you an example: If the list was longer than wide
As the list is supposed to be endlessly long and the decimal (or other
base) representation of each member is supposed to be endlessly "wide",
why should either endlessness be greater than the other?
Cantor's diagonal proof does not prove that all numbers of the list are
included.
Perhaps not to you, but it does to most.
That is not an argument for truth, rather the opposite.
There are those to whom the truth is anathema.
"Mueckenh" seems more and more to be one of them.
If so, then his rejection of a statement would be rather more evidence
of its truth than its falsity.
The society of mathematicians is limited of those who agree to accept
whatever is proved according to certain generally accepted standards of
logical proof and not to insist on things whose proofs cannot meet that
standard.
The diagonal proof is not valid for an infinite list. There is no
definition at all by Cantor. He only stated continuation.
On the contrary, Cantor, and others, have specifically defined valid
rules for constructing a real number not in any given list of real
numbers.
You reject things that have been proved within that standard and insist
on things whose proof does not meet that standard.
Same did Cantor 130 years ago.
Only in your opinion, not in fact. And your opinions have proved flawed.
So that what you claim is not acceptable as mathematics.
Either equal rights for all or for none.
Standards of proof are not democratic.
Correct. And your arguing few lines above about the society of
mathematicans is nonsense.
It is mathematicians collectively who decide what mathematics is, the
rest of the world does not have a vote. And you are one of those with
no vote.
Then the set of rationals never becomes naturally ordered, which would
require exactly what you say never occurs.
Hence there must be one assumption which is wrong, isn't it?
The assumption that any sequence of transpostions can convert a well
ordered set into a dense set, or vice versa.
That is the result. Which is the wrong assumption?
Hence there must be one assumption which is wrong, isn't it?
The only assumption I made is the existence of infinite sets.
You also assumed that you could convert between dense ordering and well
ordering by a sequence to transpostions.
That is the result. Which is the wrong assumption?
Do you have an idea why? (What is wrong with my assumptions?)
You assumed, in contradiction to what Cantor said,
that you could
convert between dense ordering and well ordering by a sequence to
transpostions.
That is the result. Which is the wrong assumption?
The assumption that that result can be valid is wrong in the face of the
proofs that it is not valid.
.
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