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YOU are better than YOU think. Show
yourself how:
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Logic
chapters 1 to 5 re- appear not in sequence, as is or longer,
in Volume 1A, Pattern Based
Reason, Bon Appetite.
Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
Logic
mastery makes the hard, easier. Logic
mastery leads to better, stronger and richer comprehension. Logic
mastery improves reading and writing. Logic
mastery ease learning difficulties. Logic
mastery gives a headstart. In sum, logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
liinear Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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Caution: Site advice is approximately
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What may be learnt and when depends on how skills
and concepts are developed. Making the hard easier and clearer will allow
earlier & richer development of skills and concepts.
Try the Twiddla
Whiteboard. In principle, it allows
to people to draw and chat together online on a copy of this webpage or a clean
sheet. The chat may be via text or audio. Visit www.twiddla.com
to set up whiteboards to work with the webpage of your choice.
For online automated help in senior high school maths & calculus,
visit quickmath.com For Automatic
Calculus and Algebra Help with derivatives, integrals, graphs, linear equations,
matrix algebra, visit calc101.com
With overlap, each site quickmath
& calc101offers a different range of
services, some free, some not, all based on webmathematica. Good luck.
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Previous: Chapter 5, Deception
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.
Arithmetic, algebra and geometry give many neutral examples for this. The
examples below involve no mathematics. Bon Appetite.
Chapter Subsections: [ Direct and Indirect Usage of a Single Rule ] [ Linking and Chaining Two Rules Together ] [ Linking and Chaining Several Rules Together ] [ Deductive, Inductive or Empirical Reason ] [ Chapter 6, Chains of Reason (Deductive Reason), Pattern Based Reason ] [ Linking and Chaining ] [ Putting Several Rules Together ] [ Deductive ]
Next: Direct and Indirect Usage of a Single
Rule
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www.whyslopes.com
Volume 1A, Pattern Based Reason
Chapters 1 to 24
FOREWORD
Three Remarks
1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive
& Empirical Views of Mathematics
15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways
18. Waking up
19. Symbols & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again
To reason often means to persuade someone of
the need for an idea or action. That someone could be yourself. So be
careful.
Vol 1A Postscripts
- online only
+Proof by
Absurdity alias proof by contradiction
+How the demand
for consistency supports the law of the excluded middle
There is a difference between
knowing how to spend money,
and having money to spend.
There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.
.
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