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YOU are better than YOU think. Show
yourself how:
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Read logic
chapters 1 to 5 in online volume Three
Skills for Algebra for greater skills & confidence
in work
and study.
Learn to read notes and textbooks like
a lawyer, so that no nuance, no subtlety and no clause escapes your
attention. |
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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
correct, for some circumstances, not all. That leaves room for thought |
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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 17, part II, Yours
Objectively
The Discovery Process
Rules and laws often begin as a suggestion or a possibility that someone
wanted to accept or investigate. The direction of exploration and one's
inclinations on what to examine is subjective. It depends on personal experience
and knowledge. But the reproducible and repeatable results of any such
exploration and examination are objective.
Putting patterns or implication rules together is like putting together the
pieces of a jigsaw. Except that some, if not all, of the pieces of this jigsaw
puzzle are upside down; you are not sure that all are from the same puzzle, and
you are not sure that some subset of them will form a complete picture. The
organization of the pieces and the discovery of results from them take time.
The process of discovery of a new idea and the putting of all the pieces
together sensibly may be long and painful. It may require imagination or acts of
desperation. At many points in the discovery process, we may want to quit. Moral
may be low. The chances of success seem low. The moment of discovery puts the
past in perspective. Once the way to accomplish something is discovered,
repetition often appears trivial (easy). This appears as an anticlimax. A large
difficult step has suddenly become small. It is time for a new problem.
The discovery of useful new chains of reason is not obvious, especially when
you are the first to explore the problem area. Once found, the repetition of a
chain of implications is often much easier. For example, all of us have looked
for a lost object. The lost object is in the last place we look, and once it is
found we may think to ourselves I should have looked there first.
Beforehand, we could not have known better. Similarly, when we look for useful
chains of implications, the search itself may be difficult or harder than we
wanted, thought or expected. Once the useful chain has been found, we may feel
with our usual hindsight that the search could have been simpler. The split or
dichotomy in our thoughts is as follows. What is unknown is hard. What is known
is easy or trivial. The whole process of learning and exploration consists of
making a hard puzzle easier, or a previously unknown path, easy to follow or
repeat.
With implication rules, when we try to reach an attractive or useful
conclusion that has not been proven before, there is no guarantee that we can
reach the desired end. Implication rules are clues in a detective mystery. In
unfolding or unraveling such a mystery, the trail of implications can lead to
unexpected places or nowhere. Persistence, intelligence and luck are required.
Next: Chapter 18, Self and
External Awareness Awaking Etc
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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.
1A Logic Postscripts
- online only
+Proof by
Absurdity alias proof by contradiction
+How the demand
for consistency supports the law of the excluded middle
+Reality versus or with the aid of Imagination
+Links for reason, logic and crtical thinking
+Three Remarks
+History
Lost or Missing
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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