Employ an online or offline tutor at your own risk from
AU:
tutorfinder.com.au
CDN : findatutor.ca
CDN: .i-tutor.ca
CDN: Montreal Tutors
NZ: findatutor.co.nz
UK: tutorhunt.com
UK: tutors4me.co.uk
USA: wiziq.com
USA: ziizoo.com
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YOU are better than YOU think. Show yourself how:
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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
Do not leave here without it - Logic
mastery will develops critical thinking, improve reading and writing,
and give a firmer base for work and studies at many levels. Good luck.
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Caution: Site advice is approximately
correct, for some circumstances, not all. Site How-TOs are logically
developed, but not tried and tested. That leaves room for thought and
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After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
linear2007 Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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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Explore collaborative whiteboards from
groupboard, twiddla or
scriblink.
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Chapter 4
Repeatable & Reproducible Results
Previous: One- Versus Two-Way Implications
When we do arithmetic, we follow rules. If each of us does not make a
mistake, we will get the same result as each other. Each calculation is
reproducible. Other people know how it was done. They can repeat it, and see if
they agree with our results. When we get a result by following rules or
instructions, other people can check our results. All they have to do is follow
the same rules.
Just as we have methods for doing arithmetic carefully and precisely, we also
have suggested methods for thinking carefully about what to accept, to do or to
decide. The ability to read and understand rules or suggestions precisely is
needed not only in persuading ourselves or others but also in following recipes,
instructions and rule-based reason.
The suggestions or rules which give repeatable and reproducible results are
the most certain and possibly the most correct. Reliable rule-based processes
give repeatable and reproducible results. These results do not depend on who
gets them. For instance, a good recipe can be followed by any cook - provided
the cook can find all the ingredients. Results should depend on the recipe, but
be independent of the cook.
Chapter Subsections: [ First Puzzle ] [ Second Puzzle ] [ One- Versus Two-Way ] [ Talking About Logic ] [ Implications vs Suggestions ] [ One Versus Two Way Committments ] [ Repeatable & Reproducible ] [ Limits and Benefits ] [ Accidental Rules ] [ Steps for Better Reason ]
Next: Limits and Benefits
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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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