Re: abundance of irrationals!)

Randy Poe said:
>
> aeo6 Tony Orlow wrote:
> > Randy Poe said:
> > >
> > > mueck...@xxxxxxxxxxxxxxxxx wrote:
> > > > You see what happens then: There is no set size at all which
> could
> > > > reasonably be defined or measured in terms of consistent notions.
> > >
> > > No, we have a set of precisely defined and consistent
> > > concepts which are easily grasped by anyone with even
> > > the bare bones of a logical mind.
> >
> > As long as you abandon any logic
>
> You suffer the same soplistic problems Mueck does: You
> can't follow the reasoning which is crystal-clear to
> all of us.
>
> Therefore "there is no logic".
>
> Here's a clue: Sometimes fields of study exist and
> are useful even if you don't understand it. I can't
> understand what 90% of the people in an investment
> house do, but I accept that they earn their money.
>
> - Randy
>
>
You also don't seem to understand information theory or infinite sums, and you
also seem to like to chop out the part of a sentence you don't like when
quoting people. Here is what I actually said:

"As long as you abandon any logic not contained in the axioms you have etched
in your particular stone, including anything from any other areas of math."

Now, what is "crystal clear" to you given the axioms of cardinalty may be true
for those axioms, but those are not the only axioms in the world, and no axiom
is guaranteed to be true any more than a scientific theory is. If we observe
that a system produces unexpected results, we need to detect the contradiction,
either in our expectations, or in the system which produced the results. In
science, this is equivalent to an unexpected experimental result being due to
either a problem in our theory, or in our experiment reaults.

Here's a clue: Sometimes we need to look outside our local axiomatic
neighborhood and see how our little community gets along with those around it.
Cardinality has a wall around it.

I have disproven the obvious fallacy of an infinite set of finite naturals.
Please comment on the proofs, but don't waste my time. Tell me why it is not
appropriate to apply information science to strings of symbols, or infinite
series to the sum of an infinite set of intervals, and use those concepts when
discussing sets of those kinds of objects.
--
Smiles,

Tony
.

Relevant Pages

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  • Re: abundance of irrationals!)
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