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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: Euclidean Model
for Reason.(Chapter 13)
This chapter provides several perspectives on mathematics. Some are slightly
at odds. Some are slightly technical. The next chapter Objective Processes
returns to some simpler material.
Empirical Origins of Decimal Arithmetic
The rules of arithmetic and our notation for fractions and decimal numbers
which we use today were created about three hundred years ago. The
popularization of decimal notation began with Simon Stevin (1548 -1620 A.D.)
Before the use of decimal notation, our forbears (except those using the abacus)
found arithmetic operations of +, -, ×, and ÷ very awkward to master.
Knowledge of arithmetic, like literacy, has gradually become more widespread
since the 15th century. Even at the start of the 20th
century, few people could read, write and figure. Public education has changed
this situation in many communities.
The rules of addition, subtraction, multiplication and division with decimal
notation had to be discovered or invented. In all this, trial and error or
experimentation, was used to formulate the rules and even the notation for
arithmetic. That is, the rules and methods of arithmetic, taught in elementary
school, are human creations. Despite this, they work: The results obtained from
each arithmetic operation (+, -, ×, and ÷) are reproducible and supposedly not
dependent on whom obtains them. Arithmetic methods were empirically discovered
and established. These methods were invented and then used to solve problems in
business and geometry. Reproducible and repeatable results led to a wide, if not
universal, acceptance of the methods. Calculations, precisely described, are
reproducible.
Note that arithmetic yields an alternative approach to geometry. The use of
coordinates to identify points in the plane, in fact the first quadrant, by
Descartes (1596-1650) eventually led to a geometry based on rules of
arithmetic instead of the assumptions of Euclid. Today, the two perspectives
are often mixed – a departure from the ideal of having only one basis for
geometry. The original approach of Euclid is now labeled as synthetic geometry
while the arithmetic-based approach is labeled analytic geometry.
Chapter Sections: [ 14 Set Theory ] [ 14 Before & After Set Theory in Pure Mathematics ] [ 14 Euclidean Model for Physics ] [ 14 Applied Maths and Electricity Apart from Sets ] [ 14 Decimals Absent From Pure Mathematics ] [ 14 Modern Mathematics Education ]
Next: Set Theory & the
Euclidean Model For the Codification of Mathematics
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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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