The Number Line Via PjProblemStrings Sequencing.
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The Number Line Via PjProblemStrings Sequencing

The Number Line is a great human invention. Its current state is a consequent of centuries of development of an initial primitive one-one mapping of symbols to the existential awareness of physical quantities in space. The success of the Number Line is due to its explicit and implicit values. The myriad advanced number theories are consequences of its implicit value. The cardinality and ordinality of numbers are consequences of its explicit value.

Consider the following scenarios:
Scenario I: a crane offloads the containers of an importer from a container ship one container at a time and stores them in an allocated space onshore. The importer's guard who has the identities of the containers ensures that the containers are accurately offloaded.

Scenario II: the customers of a service company que up in front of a service counter. The company's guard ensures an orderly que.

(a) Which of the scenarios involves PjProblemStrings Sequencing?

(bi) Which scenario emphasizes the cardinality of numbers?
(ii) Which scenario emphasizes the ordinality of numbers?
(iii) Explain how the guards' responsibilities are influenced by
the cardinality and ordinality of the scenarios.

(c) Consider a number line initialized via PjProblemStrings Sequencing:
(i) define the 0 (zero) of such a number line.
(ii) Interprete the positive whole numbers of such a number line.
(iii) Interprete the negative whole numbers of such a number line.

(d) The coordinates of the cartesian point A(x, y, z) is derived
via PjProblemStrings Sequencing. Explain.

The strings: S7P3A3k (force -k =1, 2), S7P4A4k (motion- k =1, 2, 3,4).

The math:
All Pj Problems are at play. However, Pj Problems of Interest are of types force and motion.

(a) Both scenarios.

(bi) Scenario I emphasizes the cardinality of numbers.
(ii) Scenario II emphasizes the ordinality of numbers.
(iii) The guard in scenario I is not much concerned about the order of the arrival of the containers to the storage space. He is mostly concerned about the identity and number of containers that arrive. The guard in scenario II is mostly concerned about the order of arrival of the customers. If the queing protocol is First In First Out (FIFO), the guard must ensure that the first customer to arrive is in front of the que and so on.

(ci) An empty space is one definition of zero. Another is the nullification of similar PjProblemStrings Sequencings into the space.
(ii) A positive whole number can be either the number of unit matter sequenced into the space or the number of the PjProblemStrings Sequencing into the space.
(iii) A negative whole number is a deferred PjProblemString Sequence.

(d) Place two feet together at the origin (the zero) of the Cartesian space. Take x unit steps along the X axis (each step is a PjProblemString Sequence); y unit steps along the Y axis and z unit steps along the Z axis and you will arrive at point A(x, y,z).

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