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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3
votes
7answers
302 views

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 ...
-2
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1answer
104 views

What is the best way of introducing set theory? [closed]

The students are aware of mathematical logic and proof but have not come across any of the notions of a set. What is the most natural and motivating way to introduce set theory?
1
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1answer
124 views

When self teaching, should I learn set theory before continuing ap calculus?

I am studying ap calculus now, before I move onto differential equations etc., but the thing I am unsure of is, should I learn set theory before continuing on my ap calculus sections?
7
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2answers
370 views

Why is set theory not taught at the outset of math education?

A beginner in math, reading Badiou, I found the following quote on set theory in Being and Event: The axiomatization consists in fixing the usage of the relation of belonging, $\in$, to which the ...
14
votes
8answers
2k views

Cognitive traps in very early set theory

As of last year, I began teaching a course in theoretical computer science, and one of the topics that we cover is sets. In particular, we go over: the actions $\cup$, $\cap$, and $-$, ...
-3
votes
3answers
550 views

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 ...
1
vote
3answers
90 views

Determining sets to show sufficiency of a condition?

$p \to q$ that means (among others) $p$ is a sufficient condition for $q$. To show the sufficiency, I teach my study by determining the set for $p$, the set for $q$ first and comparing their ...
12
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2answers
508 views

What to teach in Set Theory & Logic Course

I will be teaching a third-year introductory course on Set Theory and Logic soon and was hoping to get advice from this community. I would rate my students' proof abilities as weak and was hoping to ...
6
votes
2answers
232 views

Cartesian product set

I'm preparing a task on the Cartesian product of two sets and I have run into the following confusion: I understand that the Cartesian product is not a commutative operation. Generally speaking, AxB ...
4
votes
1answer
114 views

On using different notations for the same objects

Historically, in set theory we use two different notations to refer set theoretically same objects $\aleph_{\alpha}$ and $\omega_{\alpha}$. The folklore justification of this dual notation is that we ...
8
votes
2answers
540 views

What caused the (relatively) recent popularity of set theory?

When I was growing up during the 1960s, "set builder notation" constituted a large part of what was then the "new math." Question: When and why did "set theory" become popular in math education? ...
3
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2answers
772 views

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. ...
17
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6answers
646 views

What is a number?

In a set theoretic point of view all mathematical objects are sets. We "call" some of them as numbers (e.g. sets in $\mathbb{N}$, $\mathbb{Q}$, $\mathbb{R}$, $\mathbb{C}$, $Ord$, $Card$) but what is ...
22
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16answers
1k views

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 ...
28
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13answers
6k views

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 ...
19
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11answers
956 views

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 ...