Re: A CHALLANGE TO CANTORIANS
- From: The Ghost In The Machine <ewill@xxxxxxxxxxxxxxxxxxxxxxx>
- Date: Tue, 21 Aug 2007 20:51:20 -0700
In sci.math, neilist
<littoralee@xxxxxxxxx>
wrote
on Mon, 20 Aug 2007 07:27:38 -0700
<1187620058.439289.280910@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>:
On Aug 19, 4:57 pm, tommy1729 <tommy1...@xxxxxxxxx> wrote:
<snip>
cantor "seems" to be incomplete
Cantor *is* incomplete; Goedel proved it.
yep , and therefore also a reason to remove cantor ...
math would be so more complete without cantor ...
Tommy, how can something be "more complete"?
Easy. Any inconsistent system is by necessity complete, since
P . ~P => Q
is true for any P and Q. Granted, this is probably not all
that desirable or useful. :-)
It's either complete or
not complete in view of underlying postulates.
And Godel proved (to paraphrase) that a mathematical system cannot be
both complete and consistent.
So "math" would not necessarily be "(more) complete without cantor"
although "math" may be consistent without Cantor.
Would you prefer "math" to be consistent or complete? You can't have
both.
I like the current math just fine, myself. It's a little
weird in spots (what comes after omega sub omega in the
transfinite ordinals, for example?) but otherwise meets
my needs.
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