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Odds & Ends Group I Group II
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How Logic or Rule-Based Reason Appears in Math(c) copyright Alan Selby (aselby@cam.org) 1995. Logos is the Greek word for thought. In mathematics, the subject of logic is often met as the study of the rule-based reason. When mathematics is only described and not derived from first principles, links to logic are missed or not noticed. But it is possible to identify them. Every use of terms or phrases such as therefore, thus, hence, from this, gives, yields, etc, signals the drawing of a conclusion. Note that chains of reason are followed and conclusions may be drawn in every subject, and not just in mathematics. Any multi-step rule-based process which yields a result or a conclusion gives an example of a chain of reason. In particular, conclusions in arithmetic and in further parts of mathematics are drawn from rule-based thought processes, often recorded on paper, which are repeatable and reproducible, and thus verifiable --- independent of the person or computer following the process. This kind of reasoning or figuring met by young students of elementary mathematics. It can be noted before and possible during further lessons on algebra and geometry, descriptive or deductive. Note primary math instruction is pre-algebraic and pre-deductive, but still rule and pattern based. Further mathematics and geometry too may provide a transition to the algebraic and deductive explanation and comprehension of mathematics and its logic. |
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Road
Safety Message Do not walk on a road with your back to the
traffic - rule of thumb
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