Re: Request for Peer Review - Refutation of Cantor Theorem Conclusion

Arturo:
But no, the number I created was NOT on your list; it was not the
first number on the list you gave, because your list had as a first
number a number that began with 1. It was not the second number on
list because that number had ? in the second dposition, while mine has
something else. It was not the third number because your third number
had a 0 in the third position, mine has a 1; it was not the fourth
number because your fourth number had a 1 in the fourth position,
mine has a zero. It was not the fifth number beecause your fifth
number had a 1 in the fifth position, mine has a 0. Etc

1 - 0.00000...
2 - 0.1*100...
3 - 0.00001...
4 - 0.00010...
5 - 0.00011...
6 - 0.01011...
....

The number you created, 1*100, is #2 on the list. '*' is just a symbol
representing the contradiction 1=0 and 0=1. It is not a unique digit
because only {0,1} are allowed.

The fact that you also ignore queries
makes things difficult. I asked several questions about your
interpretations of sundry things, and about sundry statements you
made, in a number of my previous posts.

My goal is not to confuse or confound. My goals is to find a common
ground to convey ideas. I am not purposely ignoring your questions
comments to confuse. Some I choose to ignore because I believe further
statements invalid/clarify/answer your comments. For example:

You paraphrased this axiom as saying that set must be a subset of
EVERY V. That is simply not what the axiom of separation says, and not
what your quoted statement says. The axiom of separation says that for
every V, if "formula" is a property then the colleciton of all x in V
which satisfy the formula forms a set.

I made a mistake in documenting the Axiom and corrected it. I did not
answer questions about the subset because it was based on the wrong
Axiom and therefore was complete garbage. Obviously, according to the
corrected Axiom, I am not making any assertions whatsoever about a set
being a subset of every V. If that was not clear, then sorry. Strike it
from the conversation. I will endeavor to be more clear and answer each
question.

So, if you are willing, let me try a clean slate, forget previous
confusion, and I will try to map my notation to yours.

Let f be a function f:S |-> P(S); ie, f:S mapsto P(S).

Let V be a variable that represents any level. A specific level will is
specified by _n, such as V_0.

Let C be the set C = { x : x in S and x in V and x notin f(x) }. This
is the set used in Cantor's Theorem. It is sometimes referred to as the
diagonal set. Because another set also is referred to by that name, let
us just refer to it as C. Have I made any mistakes so far?

Let D be the set D = { x : x in S and x in V and x notin f(x) and
f(x)=D }. This is also sometimes referred to as the diagonal set. Let
us simple call it D. Have I made any mistakes so far?

Do we agree that D subset C?
Do we agree that D is the set that causes the contradiction? That if I
define the following set

Let E be the set E = { x : x in S and x in V and x notin f(x) and
f(x)!=E }

that no contradiction is generated?

Let F be the set F = { x : x in S and x in V and S=V and x notin f(x)
and f(x)=F }. This should be a valid set that generates a contradiction
just like D.

Now can I not make the jump:

F = { x : x in V and x notin F }?

Returning to C, is it not a consequence of C that there exists a y such
that (y subset P(S) and y notin S)?

And in the case of F there exists a y such that (y subset P(V) and y
notin V)?

Axiom Schema of Separation: (forall X)( Y = { u : u in X and f(u,p) }
). Is this correct?

Hopefully, up to this point, we are in agreement?

.

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