Monthly Archives: November 2012

Teaching Fractions books low sales rank Amazon

If one goes to the Amazon site, and searches for teaching fractions and selects books as type, and selects relevance, the books that are serious books on teaching fractions have few reviews and low sales rank. Thus we see nihilism … Continue reading

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Dedekind 1888 What are and what should be the numbers is music of structural math

Axiomatic set theory books and foundation of math through logic books are mostly difficult symbolic jungles that leave the reader without inspiration.  Many readers will come from these books feeling that understanding the structure of elementary math is beyond them. … Continue reading

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Cyberchase teaches multiplication is repeated addition

http://en.wikipedia.org/wiki/CyberChase http://en.wikipedia.org/wiki/List_of_Cyberchase_episodes ==Excerpt 19 Send in the Clones February 14, 2002 The kids persuade Cy Clone to capture the clones of Delete that are causing chaos in R-Fair City. Multiplication – Stuck on a multiplication problem? Relax! Remember that multiplication … Continue reading

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Symbolic math proofs work best when you know the proof already

Symbolic math proofs are hard for most people to follow.  This particularly applies if they are lost. When they understand in words what the proposition being proved is, and understand in words the idea of the proof and better yet … Continue reading

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Recursive definition “set theory”

recursive definition “set theory” http://www.saylor.org/site/wp-content/uploads/2011/06/Recursion.pdf http://www.math.ku.edu/~roitman/stb3fullWeb.pdf “recursive definition of sets” http://en.wikipedia.org/wiki/Recursively_enumerable_set http://www.cl.cam.ac.uk/~lp15/papers/Sets/set-II.pdf http://math.stackexchange.com/questions/138807/set-theoretic-function-definition-recursion-theorem  

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More on finite axiom of choice

http://mathoverflow.net/questions/4669/can-we-disallow-finite-choice Finite, counted and finitely indexed are discussed as terms in the above as well as choice functions in such cases.  This covers not just a single choice from a set, but a map from a head segment into a … Continue reading

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Trichotomy injections for finite sets

Suppose we have defined finite sets.  In the prior post these are sets with a bijection to a subset of a head segment of the natural numbers. For finite sets, can we prove trichotomy of cardinality comparisons? For finite sets, … Continue reading

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