**Description: **Define plus infinity.
Note that the definition is arbitrary, requiring
only that
be a set not in and
different from
(df-mnf 7121). We use 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 7125
and mnfnre 7126, and we'll also be able to prove .
A simpler possibility is to define as and
as
, 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.) |