# Tag Info

## Hot answers tagged set-theory

22 votes
Accepted

• 4,850
8 votes

### How can I convince my brightest student of Cantor's theory?

Here is another attempt. Consider the function $f:\mathbb{N} \to \mathbb{R}$ defined by $f(n) = \textrm{ The number of elements in the set$\{n,n+1,n+2,...2n\}$}$. In other words $f(n) = n+1$. ...
• 20.7k
8 votes

### Cognitive traps in very early set theory

I think your specific situation with the exam question is similar to a pre-Calc class that spends a good amount of time on solving trig equations, but then asks on the exam for the student to write ...
• 6,514
8 votes

### How to motivate equivalence classes

As a simple illustration of the most basic case, $\mathbb{Z}/2\mathbb{Z}$, I sometimes push the light switch of the classroom about a dozen times in a row, too fast for them to count. Then I ask: &...
• 8,731
8 votes

### Cartesian product set

They are isomorphic. While $A\times B \neq B \times A$ for any arbitrary distinct sets $A$ and $B$, by defining the map $\phi:A\times B \to B \times A$ by $\phi(a,b)=(b,a)$, we can show that ...
• 2,584
7 votes

### Examples of cultural limitations on math education

Perhaps this historical example fits the bill: Khovanova, T., & Radul, A. (2012). Killer problems. American Mathematical Monthly, 119(10), 815-823. The piece was published earlier on the arXiv ...
• 18.2k
6 votes

### Cognitive traps in very early set theory

I think the issue here is really more one of problem solving skill or abstraction ability. You could see the same thing in various problems in computer science or in college algebra where some ...
• 81
6 votes

### Determining sets to show sufficiency of a condition?

I would not recommend to teach this method since there are some downsides. Take $A(x) \iff x \text{ is divisible by } 2$ $B(x) \iff x \text{ is divisible by } 42$ Is $A(x) \implies B(x)$ or \$B(x) \...
• 1,981
6 votes

### Determining sets to show sufficiency of a condition?

First, although you talk a bunch about cardinality, I don't see how that makes sense, so I'm going to assume you mean that you have them determine if the set corresponding to p is a subset of the set ...
• 11.3k
6 votes

### Cartesian product set

I like Chris C's answer; I will offer another point of view. Perhaps the difficulty lies in the example that has been chosen: a deck of cards isn't naturally a cartesian product for exactly the ...
• 3,627
6 votes

### What is a number?

Whatever teachers may think about the nature of numbers, the foundations of "arithmetic" and the nature and concept of number in particular are very subtle. For a recent and sophisticated look at the ...
• 1,822
6 votes
Accepted

### Category mistakes regarding symbols and their impact on math (mis) understanding. ( Object symbol/ sentence symbol confusion)

I like the idea here, but I agree that it misleads students, and might have the opposite of intended effect. Why not hand out a paragraph to the students, and ask them to critique it. Say that the ...
• 20.7k
6 votes

### Mnemonics to correlate the definition of "asymmetric relation" and "antisymmetric relation" with the terms

First, let's note that the terms as used by Rosen are standard definitions, as we can see on Wikipedia (here and here), as well as other resource sites. There was some question about this in the ...
• 21.3k
6 votes

### Is it considered a mistake to use different correct notation for writing intervals?

In theory you could choose to define a notation such as $$(a, b) = \{x ; b < x < a\},$$ but why would you do it? It has exactly the same power as the usual notation, and now the reader either ...
• 4,746
5 votes

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

Because many worthwhile topics in math don't require set theory to learn them and apply them. You can get a lot of good stuff done with arithmetic, algebra, trig, calc, etc. that is uninformed by set ...
• 295
5 votes
Accepted

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

Short answer: No. If you really want to know a little bit about sets, the first section of Book of Proof or Applied Discrete Structures would more than suffice for the purposes of most collegiate ...
• 5,750
5 votes

### Fun set theory for kids

A great way to get folks engaged is to bring up a contentious question. Here's one: What's the 0th power of a whole number? In particular, what's the 0th power of 0? Like Lorenzo Najt mentioned, ...
• 419
4 votes

### How to motivate equivalence classes

To be honest, I wasn't sure to write this answer or not, since it was hard to choose what to write about! Believe or not, my whole PhD thesis entitled "Equivalence" was to provide a ground for ...
• 4,314
4 votes

### What is a number?

I think this question is important. I'd love to see an actual answer to it and cannot upvote it enough. I don't have an answer, but would like to share some intuitions/speculation. I think the ...
• 5,857

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