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Addition and Subtraction are premier concepts in the physical universe. The creation of the universe would have been impossible without addition and it will be impossible to end the universe without subtraction. The sequence of PjProblemstrings that represents addition and subtraction reveals a deeper understanding of the concepts beyond the symbols humans have created to represent them.

(a) Describe the sequence of PjProblemStrings that add matter to an arbitrary space with a containership property.

(b) How is the sequence of PjProblemStrings for addition different from the sequence of PjProblemStrings for subtraction?

(c) True or false? whenever there is an addition of matter into a given space, there is a subtraction of matter from another space.

(d) Indicate the addition and substraction in the following scenarios:
(i) A fisherman catches a beautiful fish with his fishing line and quickly returns the fish into the river.
(ii) Putting the golf ball into a hole.
(iii) An airplane in flight.

(e) Consider a game of chess. Which piece on the board is most able to visit different spaces on the board?

The strings: S₇P₃A₃₂ (Force - Push).

The math:
Several Pj Problems are at play. However, Pj Problems of Interest is of type force (pull and push).



(a) Given an arbitrary space with a containership property, the sequence of PjProblemStrings that add matter to the space is force-motion-force. The force may be a pull or a push and the motions associated with the force may be any of the four types of motion (linear, rotary, reciprocal, oscillator). The first force fetches matter and places it in space of interest . The second force keeps the matter in the space even if just transiently. Addition and subtraction results in change.
So,the sequence of PjProblemStrings = S_iP₃A_k S_iP₄A_k'S_iP₃A_k.
Where S_i is an arbitrary space (assume to be the same space in the sequence. it may vary).
Where, for the force, k = 1, 2 (pull, push)
and for the motion, k' = 1, 2, 3, 4 (linear, rotary, reciprocal, oscillatory).

(b) The sequence for subtraction is also force-motion-force. The first force removes matter from space of interst and places it in another space. There is no difference in sequence but there is difference in force objective. So, the types of force and motions may vary.

(c) True. This is the add-substract duality. An addition to a space implies a subtraction from another space (also conservation of mass).

(d) (i) Fisherman subtracts when he pulls fish out of river and adds to the space the fish is pulled into. Fisherman adds when he pushes fish back into the river and subtracts from the space from which the fish is pushed.
(ii) The golfer subtracts from where he putts the golf ball and adds to the hole into which the golf ball enters.
(iii) The airplane is serially added and subtracted from the coordinates that constitute its flight path. In essence, motion is a series of spatial addition and subtraction.

(e) The queen because she has the greatest degree of motion freedom. In general those with the greatest degree of motion freedom are most able to visit different spaces.

Blessed are they that have not seen, and yet have believed. John 20:29

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