Re: collatz conjecture -> a * p(a)
- From: Dave Seaman <dseaman@xxxxxxxxxxxx>
- Date: Sat, 12 Jul 2008 13:31:39 +0000 (UTC)
On Sat, 12 Jul 2008 07:21:20 EDT, T.H. Ray wrote:
"Mark Nudelman" <markn@xxxxxxxxxxxxxxxxxxxxx> writes:
I'd be confused at best if I took either stance,because a perfectly
consistent system can be constructed either with orwithout AC. So
there is no basis for believing or disbelieving it.
A perfectly consistent system can be constructed with
or without the
axiom "ZFC is inconsistent". Does this mean that
there is no basis for
believing or disbelieving that ZFC is inconsistent?
In fact, there is no meaning to the statement thatAC is true.
Sure there is. That the axiom of choice is true means
that every set
of non-empty sets has a choice function.
It also implies that every vector space has a basis. I'd say that's
pretty important.
Which does some violence to the meaning of "function,"
if we want a mathematics of non-arbitrary boundaries.
What choices are forced upon us?
How do you "do violence to the meaning" of something without changing its
definition? AC does not redefine "function"; it merely guarantees that
certain functions exist. Without AC, we don't know that those functions
do not exist; their existence is merely undecidable.
AC may well be a useful fiction, as was the fifth
postulate of Euclid for geometry.
What part of mathematics is not a "useful fiction"? Maybe some parts are
not useful (yet).
--
Dave Seaman
Third Circuit ignores precedent in Mumia Abu-Jamal ruling.
<http://www.indybay.org/newsitems/2008/03/29/18489281.php>
.
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