Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

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**:
S_{7}P_{3}A_{3k} (force -k =1, 2), S_{7}P_{4}A_{4k} (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).

Math

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.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

Absolute Value Functions

Conics

Real Numbers

Vector Spaces

Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

Advanced Calculus - Jacobians

Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings