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Chapter Sections: [Chapter Intro ] [Conclusions
From a Single Implication] [Linking
and Chaining Implication Rules] [ Deductive
Reason]
This chapter shows how reliable rules and patterns can be
directly employed one at a time, or one after another, to get conclusions or
further reliable rules and patterns. The question of what rules are reliable
is considered in the following chapters.
Rules used to get or suggest conclusions are called implications. Just as there
are methods for adding and multiplying numbers carefully, there are also methods
for using implication rules by themselves to get conclusions. There are also
methods for linking, threading and chaining implication rules together to get
more implication rules. This chapter uses examples to explain two basic ideas:
- how to directly use a single implication rule to get conclusions, and
- how to link, chain or thread implication rules together to obtain or
derive more rules and more conclusions.
The examples are not important (and are perhaps ridiculous) but they illustrate
some rule-based methods in reason. Examples which involved real-life situations
might distract from mastering these methods. That is, in real-life situations,
each of us may have opinions or prejudices about what should occur. That could
spoil an explanation of the use and linkage of implication rules. There is a
need for neutral examples to illustrate the use of implication rules one at a
time or one after another.
Chapter Sections: [Conclusions
From a Single Implication] [Linking
and Chaining Implication Rules] [ Deductive
Reason]
Next Section: Conclusions
From a Single Rule
Next Chapter: Longer Chains of Reason
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Three Skills
For
Algebra
understanding & explaining
Reason and Math
Volume 2
Printed in Canada
ISBN 0-9697564-2-9
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[ Back ] [ Home ] [ Next ]
Chapters and Appendices
Home
Postscript: The 4-th Skill For Algebra
Foreword
1. Introduction
2. Implication Rules
3. Chains of Reason
4. Romeo and Juliet
4. Induction Mathematical
5 Knowledge Islands
6 Old Language
7 Arith Skill Check
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable
9. Algebra Talk
10 Two More Skills
11 Why Shorthand
12 Shorthand Usage
13 What's Next
14 Compound Interest
15 Linear Equations
PS I. Distributive Law
PS II. Polynomials
16 Painless Proofs
17 Pythagoras
18 Rules of Algebra
19 Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums
23 Summation Notation
24 Your Money
25 Induction & Recursion
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
A. Advice For Learning
Words Before Symbols:
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
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