Questions tagged [set-theory]
For questions about set theory topics typically studied at the advanced undergraduate or graduate level. These include cofinality, axioms of ZFC, axiom of choice, forcing, set-theoretic independence, large cardinals, models of set theory, ultrafilters, ultrapowers, constructible universe, inner model theory, definability, infinite combinatorics, transfinite hierarchies, etc.
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How to motivate equivalence classes
Equivalence classs are very useful in mathematics, but many of the applications require further background, like quotient spaces in topology or quotient groups in algebra. One good example is residue ...
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Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)
A friend of mine that teaches math has made many times the following experiment :
drawing two circles on the blackboard representing two sets A and B such that A and B are disjoint
writing on the ...
user12295
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What do you say to students who want to apply Banach-Tarski theorem in practice?
Once when I was talking about Banach-Traski theorem (paradox) I said:
OK! This is Banach-Tarski's theorem which is against our intuition but provable from our intuitive axioms! It says you can ...
user230
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How can I familiarize elementary school students with infinities larger than $\aleph_0$?
Cantor's discovery of the existence of more than one infinity was a revolutionary change in human knowledge. He defined the notion of counting by bijections and showed that one can use infinities as ...
user230
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Examples of cultural limitations on math education
Based on Maggie Koerth-Baker's article, "What do Christian fundamentalists have against set theory?", it seems there are some parts of culture which put some restrictions on math education.
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user230
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How can I convince my brightest student of Cantor's theory?
At the end of the mathematical high-school education I usually introduce the easiest facts of set theory: counbtability and Cantor's proof as the basis of modern mathematics. Now my brightest student ...
user8455