Description: Define plus infinity.
Note that the definition is arbitrary, requiring
only that
be a set not in and
different from
(df-mnf 7957). We use ![~P ~P](scrp.gif) ![U.
U.](bigcup.gif) to
make it independent of the
construction of , and Cantor's Theorem will show that it is
different from any member of and therefore . See pnfnre 7961
and mnfnre 7962, and we'll also be able to prove .
A simpler possibility is to define as and
as
![{ {](lbrace.gif) ![CC CC](bbc.gif) , but that approach requires the Axiom of
Regularity to show
that and
are different
from each other and from all
members of .
(Contributed by NM, 13-Oct-2005.)
(New usage is discouraged.) |