Category Archives: Natural Number Point Sets

Zermelo Construction of Natural Numbers Bracket Chain

Enderton Set Theory page 67 tells us that the construction null {null} {{null}} etc. is from Zermelo 1908. Von Neumann then switched to the list version. Another book indicates variants on these whose base set is the null set and … Continue reading

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Natural Numbers Cycle Challenge

Proving that the natural numbers don’t contain cycles starting from the Peano Axioms is harder than it sounds.  David Groisser’s notes call for students to try to find a simpler way.   Rips, Bloomfield and Asmuth say that no cycles in … Continue reading

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Simple Natural Number Geometric Measure Length

The number first geometric measure second approach is discussed here in terms of natural numbers.  We consider the case of length first. We are dealing only with natural numbers. No fractions and no signs.  We have a number line with … Continue reading

Posted in Jennifer Asmuth, Lance Rips, Length for Pre-Service Teachers, Length of Natural Number Point Sets, Math Ed Psychology, Natural Number Point Sets, Number classes, Object oriented concepts, PCK dependence on math foundations, Pedagogical Content Knowledge, Pre-Service Teacher Math Education, Uncategorized | Leave a comment