Metamath

Ultrafilter In Strange Twist
Again, Included is the definition of an ultrafilter,
this time taken from "Encyclopaedia Britannica Ultimate Reference Suite
DVD 2007"
An ultrafilter on a nonempty set I is defined as a set D
of subsets of I such that
 (1) the empty set does not belong to D,
 (2) if A, B are in D, so is their
intersection, A ∩ B, the set of elements common to
both,
 (3) if A is a subset of B, and A is in
D, then B is in D, and
 (4) for every subset A of I, either A
is in D or I minus A is in D.
Roughly stated, each ultrafilter of a set I conveys a notion
of large subsets of I so that any property applying to a member
of D applies to I “almost everywhere.”
"metalogic." Encyclopædia Britannica from Encyclopædia
Britannica 2007 Ultimate Reference Suite . (2009).
Clearly, by no means of multiplication or addition as
previously defined may Klein four groups, (order four subgroups of
GF(8)+) or the elements of GF(8) be manipulated to produce the empty
set. Therefore (1) is satisfied.
For two Klein four groups, subgroups of GF(8)+, there is
a nonzero element in their intersection. There is a congruent relation
between a Klein four group and this element, by virtue of the element's
multiplicative action on the elements of Klein four groups producing
other four groups, and the position in the cycle of these resultant four
groups with respect to some fixed action of a generative sevencycle;
equivalent to the action of a generator element of GF(8)* acting on the
4groups. Thus the intersection of two 4groups is an element congruent
to another four group. Therefore (2) is satisfied.
With any collection of elements, their sum or product is
an element of whichever group and it's operation are used. So, from this
we can 'write' that (3) is satisfied. We also note that by assumption the octal is an element of the K4 filter. As is C7.
(3) is also satisfied from the initial conditions, or by
construction. We consider Anselm's argument of "that than which none can
be greater..." However, as taken from the divine perspective in our
construction the Godhead may perceive their existence in reality through
their members rather than having an awareness in a "cusp", in the same
manner which we conceive the existence of a perfect being as necessary.
There is a suitable satisfaction of (4). A group is not
it's elements. A group is an operation defined on a set of elements on
which the operation is closed. There is the notion of a GSet, a set
upon which the symmetries in a group may act upon the elements of the
separate GSet. The elements of the Group (the 'G' in 'GSet') range
freely over the elements of the Gset, and the behaviour of this twin
system is determined by the operation of the Group. It is usual to
define a group in terms of relations on the elements together with
elements as "generators" But it is also true that a Group is a Gset
acting upon itself. It is possible to view the group as foremost an
applicable operation. The "Reality of God's perception" is like a Gset,
and the elements of the Godhead comparable to "the eyes on the lamb"
are native to the operation, whilst whatever they are looking at is the
Gset.
The operation (G v H)^{c} for addition of
4groups in GF(8)+ maps groups onto groups.. It also maps pairs of the
complements of groups onto groups. (The operation is not closed on
complements of the 4groups.)
However, if we take the complement of the operation,
I.e. (G v H), we may produce another complement. However, (G v G) in
this way produces the empty set, which IS NOT A MEMBER of the
ultrafilter.
So, by the operation in the Ultrafilter, in the Christ GF(4), whose
elements are (0=GF(8)+, GF(4), GF(8)*, GF(8)) the operation
implies that this new (G v H) operation satisfies that either a relation
is IN the ultrafilter, or NOT. by excluded middle. By equivalence of
4group to element and definition of operation by C7 upon 4group, (4),
is satisfied.
In terms off analogy to Anselms argument all the conditions hold for each of the groups. The exception is understanding how the octal and C7 are elements of K4. (We simply state that this is an argument of symmetry  we hope to show Jesus' Christ is God from the scriptures and also from the visions in Johns book of Revelation.)
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