FOM: ordered pair: Bourbaki
Andrzej Trybulec
trybulec at math.uwb.edu.pl
Tue May 4 09:03:19 EDT 1999
On Sun, 2 May 1999 Vedasystem at aol.com wrote:
> The Bourbaki's approach to introducing notation
> for ordered pair is preferable because one cannot prove
> silly theorems like (x,y) U {x} = (x,y).
One cannot prove it anyway
(x,y) U {x} = {{x},{x,y}} U {x} = {{x},{x,y},x} =/= (x,y)
by regularity.
You might think about an ordered pair as somthing consisting of
unordered pair {x,y} and the order { (x,x), (x,y), (y,y) }
To avoid vicious circle, you may substitute in {x,y} the corresponding
lower sets. You get
{ {x}, {x,y} }
for triple (x,y,z)
{ {x}, {x,y}, {x,y,z} }
And for (x)
(x) = {{ x }}
Now:
(x,y) U (x) = (x,y)
says that the union of a subset of a poset and the poset is the poset.
What's wrong about this.
Andrzej Trybulec
More information about the FOM
mailing list