Chapters and Appendices

Book Entrance

Islands Without Roads Between
Rooms Without Doors Between

Foreword
1. Introduction
2. Implication Rules [4]
3. Chains of Reason [3]
4. Induction Mathematical
4. Romeo and Juliet
6  Old Language
5 Knowledge Islands [2]
7  Arith Skill Check [4 X 2]
Arith Webvideos
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable [8]
9. Algebra Talk [7]
10 Two More Skills[5]
11 Why Shorthand
12 Shorthand Usage [10]
13 What's Next
PS: The 4-th Skill For Algebra
14 Compound Interest [6]
15 Linear Equations [5]
16 Painless Proofs
17 Pythagoras
PS I.  Distributive Law
PS II. Polynomials
18 Rules of Algebra [20]
19  Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums [2]
23 Summation Notation
24 Your Money [3]
25 Induction & Recursion [4]
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
Pathways for Learning

Would you like to show yourself or others how to be  algebra power users?

What is a Variable?
Introduction
Variation between Examples
Variation of Letters
A letter denotes a variable
Cases of Double Variation
Three Notions of a Variable
Constants, Parameters
& Variables
Talking about numbers
Dependent or Independent
Variable, a Matter of Choice

Chapter 5, Islands and Divisions of Knowledge

Previous Section: Islands Without Roads Between

Rooms Without Doors Between

Implication rules are also like doors or gates between sections of a building or estate. (Implication rules like doors join the rooms of a large palace, castle, house or prison. ) Some allow two-way passage. Others permit only one-way passage. All this can be a deliberate design or it could be due to a poor design.

When we restrict our paths to two-way doors, we can always retrace our steps exactly and get back to where we started. But one-way doors are different. To get back after going through a one-way door, we need to find another route back through some other door or doors. Otherwise, we are shut out of our starting room. That is, we suppose a one-way door can only be opened from one side, and that after use it snaps shut. When we go through a one-way door, we can get back to our initial side of the door only if there is a route back. But by passing through one-way doors, we may find ourselves locked out of the initial room we were in. We may further find ourselves locked in another room or section of the building.

Ignored Rooms

Whenever the building we are exploring has sections closed off or unreachable, we can ignore all maps of those sections. Making a map of the unreachable sections is not possible, except by guessing. Guessing is suggestive, yet not reliable.

Chapter Sections: [ Up ] [ Islands Without Roads Between ] [ Rooms Without Doors Between ]

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