Re: Question about set definition

On Oct 24, 2:57 pm, magi...@xxxxxxxxxxxxxxxxx (Arturo Magidin) wrote:
In article <1193255099.414172.128...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,





<agapito6...@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)
======================================================================

Arturo Magidin
magidin-at-member-ams-org- Hide quoted text -

- Show quoted text -

Thanks Dr. M. Is that a generally accepted convention? It would
appear to be confusing, since much effort is expended in asserting and
proving that certain entities are not sets, while the empty set
obviously is? In this case we seem to be saying that if we run into
something which is not a set, we agree to call it 0, and to assign it
all its properties.

It's almost like saying that if we run into the expression x = 200/0,
we will say x = 0.

Thanks again,

.

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