Re: Question about set definition
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Wed, 24 Oct 2007 19:57:37 +0000 (UTC)
In article <1193255099.414172.128950@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<agapito6314@xxxxxxx> wrote:
In Suppes' book on axiomatic set theory he defines the expression:
B= {x : S(x)}
as meaning either:
a) Set B exists containing precisely those elements that satisfy S(x).
or
b) No set exists which contains precisely those elements that satisfy
S(x) and B is the empty set 0.
I'm not clear on b). It would appear that in that case the entity "B"
is simply not a set, which 0 of course is, by definition.
What am I missing here? Thanks.
Sounds like a convention. What he is saying is that if the expression
does not in fact define a set (e.g., S(x) = "x not in x"), then by
convention we will agree that {x : S(x)} will denote the empty
set.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org
.
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