oo can be understood properly as a direction, never completed.

But this excludes complete infinite lists and uncountable sets.

Sorry, my reader just keep crashing on loading or navigating the
diagonal argument thread. 4,700 or so items tree is too much for it I
guess.
After all it is not about the diagonal argument per se anymore but
about more important underlaying entities, so it is OK I hope to move
it into a separate thread.

On Apr 24, 12:23 am, WM <mueck...@rz.fh-augsburg.de> wrote:

oo can be understood properly as a direction, never completed.

Right. If we going by Aristotle - "a potential infinity", by physics -
"a vector". In the math the infinity is the most primitive among other
sciences: it is just a shortcut for a if-greater-than function. It
takes any argument, adds some imaginary delta to it, assign it to the
infinity and returns "noop, I am still bigger than that".
Same way the math zero is another function that subtracts delta from
the argument and returns "noop, I am still smaller than that".
Respectively infinite sets are perfectly possible in the current model
- as well as infinitely big or small numbers or numbers infinitely
close to some other numbers. It is just important to remember what
background conventions are in use while interpreting results and/or
making ongoing reasoning.

But this excludes complete infinite lists and uncountable sets.

complete infinite lists - yes, but not uncountable sets (see above)
At the same time - as was rightly pointed by many in this thread - the
math doesn't require immediate correlation with the physical reality.
If such correlation cannot be found then it means that either such
correlation indeed doesn't exist: or that our current knowledge of the
physical reality is not sufficient to find such correlation, so may be
found some day later. A great sample of it could be S-matrix.
This way no one prohibits to introduce an axiomatic definition of the
actial infinity: further denoted as A-Infinity as opposed to the
currently used in the math potential infinity or P-Infinity.
A-Infinity by its very nature has to be a contradictory construct: it
is not circular, so having its beginning and its end, yet it is
infinite at least from one end of it. By the First incompleteness
theorem we can freely add to the axiomatic set of the math and do
whatever we manage to do with such extended set. At the same time by
the Second incompleteness theorem we should not waste 5,000 and
counting posts trying to prove or to disprove the consistency of the
A-
Infinity axiom using the math itself.
As much as I aware of, A-Infinity is nowhere in the current axiomatic
set of the math. Respectively one willing to work with A-Infinity -
which is just fine by itself - is also obligated to build entire
theory based on the updated axiomatic set. Again - it is all just fine
and may lead to some interesting outcomes. It is just not allowed to
add new hidden axioms to the current system and to "resolve" all
consequences by introducing a few new symbols from Hebrew or some
other alphabet.

Are you trying to reason with WM about set theory??

Sorry, my reader just keep crashing on loading or navigating the
diagonal argument thread. 4,700 or so items tree is too much for it I
guess.
After all it is not about the diagonal argument per se anymore but
about more important underlaying entities, so it is OK I hope to move
it into a separate thread.

On Apr 25, 6:22 pm, VK <schools_r...@yahoo.com> wrote:

Sorry, my reader just keep crashing on loading or navigating the
diagonal argument thread. 4,700 or so items tree is too much for it I
guess.
After all it is not about the diagonal argument per se anymore but
about more important underlaying entities, so it is OK I hope to move
it into a separate thread.

On the contrary, I think it would be quite useful
to keep posts as yours contained in the big mother
thread... It makes for much easier ignoring.

Maybe you could try an alternative browser?

Googling for `alternative browsers' will
provide a useful link for that purpose.

On 2008-04-26, VK <schools_r...@yahoo.com> wrote:

WM is arguing with the set theory

More precisely, he is making the very specific claim that ZFC is
contradictory. However, he fails in every post to substantiate his
claim - or even to show that he understands what his claim means.

It's entertaining because he keeps pulling "principles" out of nowhere
to attempt to justify this claim that he does not even understand, and
great amusement is had by all as they show the logical consequences of
his supposed principles.

WM is arguing with the set theory

This way no one prohibits to introduce an axiomatic definition of the
actial infinity: further denoted as A-Infinity as opposed to the
currently used in the math potential infinity or P-Infinity.
A-Infinity by its very nature has to be a contradictory construct:

Correct.

it
is not circular, so having its beginning and its end, yet it is
infinite at least from one end of it. By the First incompleteness
theorem we can freely add to the axiomatic set of the math and do
whatever we manage to do with such extended set. At the same time by
the Second incompleteness theorem we should not waste 5,000 and
counting posts trying to prove or to disprove the consistency of the A-
Infinity axiom using the math itself.
As much as I aware of, A-Infinity is nowhere in the current axiomatic
set of the math.

It is in the axiom of infinity. It is in omega as a number larger than
every natural number.