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 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 non-zero 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 seven-cycle; equivalent to the action of a generator element of GF(8)* acting on the 4-groups. Thus the intersection of two 4-groups 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 G-Set, a set upon which the symmetries in a group may act upon the elements of the separate G-Set. The elements of the Group (the 'G' in 'G-Set') range freely over the elements of the G-set, 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 G-set acting upon itself. It is possible to view the group as foremost an applicable operation. The "Reality of God's perception" is like a G-set, 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 G-set. The operation (G v H)c for addition of 4-groups 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 4-groups.) 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 4-group to element and definition of operation by C7 upon 4-group, (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.)Return To Section Start Return To Previous Page