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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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Postscript: For Consistency Sake
Previous: Chapter 24
Indirect Reason Again
While we may not know that a theory or set of assumptions is consistent, or
free of contradiction, we may use the requirement for
consistency as part of the reasoning process without loss of generality
or harm we hope. That is a gamble. Logician may have more say.
Law of the Excluded Middle: A or Not A.
Let A be the statement that some situation occurs. Then a story or
theory that suggests a statement A is both true and false is inconsistent. So
for the sake of consistency in our present and further reason, we may require
and assume the statement
A AND Not A
to be false - NEVER TO OCCUR. So in our story or theory in its present and
further development, we require
A OR not A
to be true but not both at any instance (except during a brief transition
period).
So A requires not (not A) for consistency with A AND not A, and not (not A)
requires A at any instance (except during a brief transition period).
Remark: The discussion of transition time suggests
the law of excluded middle might be broken momentarily when situations are
time-dependent or place dependent. For example, in counting people in a
room that has a door, we cannot say a person is all in or all out because of
the middle possibility of a person being part in and part out. So a person has
three static states namely, in, out and partly both, and two transition
state namely, going from in to out, and going from out to in. During these
transitions, the middle state of partly in and partly out occurs for a short
or long period of time.
The CONTRAPOSITIVE.
The first situation
A AND not B
is inconsistent with the implication rule
IF A THEN B.
So in circumstance where the latter implication rule IF A THEN B. holds (is
not disobeyed), we conclude or require the first situation
A AND not B
not to occur. The non-occurrence of A AND not B in turn implies the
original implication
IF A THEN B
and the contra positive implication
IF not B THEN Not A
Since both imply not( A AND not B), the two implications are equivalent
to each other and to the non-occurrence of A AND not B.
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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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