Addition And Subtraction - The PjProblemStrings

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{3}A_{32} Base Sequence = 12735 String Sequence = 12735 - 3 - 32**

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Addition And Subtraction - The PjProblemStrings

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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**:
S_{7}P_{3}A_{32} (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_{i}P_{3}A_{k} S_{i}P_{4}A_{k'}S_{i}P_{3}A_{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 *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.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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