Re: Galileo's Paradox

In article <4579d1c7@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:


When there is a balance between one assumption and another, we are in a
position to justify one or the other. That's logic....

The same way assumption of Santa Claus balances assumption of a tooth
fairy? That's TO's logic!

There are some VERY simple definitions in set theory (either naive or
ZF, AC or not), and some of them are REALLY as simple as one can
expect: a set is called "infinite" if there exists a bijection (which
already has been completely and fully WELL defined) between that set
and at least one of its proper subsets. Period. That is all there is to
it.

Cardinality, yes, is simplistic - no argument. Very simplistic...

Math is simple (not always easy, but definitely simple).
TO is simplistic.

You don't wanna accept this definition? Good, propose
yours..."potencial infinity", "actual infinity", shminfinity: give us
DEFINITIONS, axioms to work with...and let's hope that upon checking
and re-checking, those axioms and definitions aren't shown to be
inconsistent, which has NOT been proved for ZF, AC or not AC....and
that they are sufficiently interesting to deal with, of course.

Okay, a "potential" infinite set is one where each element, like the
naturals, has a specific string associated with it, which has a
left-hand end.

If those strings do not have two ends, you have either an uncountably
potentiality or a ppotential uncountability.

After some time interchanging posts, some of these trolls/crankis begin
to REALLY believe that they have proved inconsistencies,
contradictions, etc. Just read some of Eckie's posts to see what a diet
low in potassium can do to human brain.

No one here claims any such thing.

Eckie does! WM does!

One can only claim that certain
logical constructions involved are invalid.

In matters mathematical, claims without proofs usually do not count for
much. They are called conjectures.


There is nothing wrong with expecting science to satisfy intuition.

In the way that general relativity and quantum field theory do?

And one last question from me to you: what do you think of my remark,
some 5-6 days ago, that as far as I know, NONE of the megacranks is a
mathematician? Don't you wonder about this? I don't doubt there are
mathematicians that don't like this ir that part in math, but I bet
they won't troll about it as you people do, and that's a huge
difference.
Tonio




I chose to work within computer science, after having planned to become
a mathematician, for the obvious reasons....

Couldn't cut it as a mathematician?
.

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