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• 5,883

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 ...
• 8,039

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 $f(n) = n+1$. ...
• 25.7k

Can this be a better way of defining subsets?

This answer is going to have a lot of overlap with Steve Gubkin's, but maybe a bit of a different focus. I agree with him that (1) The key issue here is understanding how vacuous cases work. (2) ...
• 5,342

Can this be a better way of defining subsets?

A potential objection: what does it mean to be able to make a set by removing elements from another set? Some students will think of removing the elements one at a time. Then there'll be ...
• 529

• 12.3k
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 ...
• 5,986

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 ...
• 287

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, ...
• 459

Where can I find the partial order relation of prerequisites of undergraduate courses in the United States?

The US has different courses at different schools. Sometimes with same name but differences in content or prereqs. It would be more meaningful to sketch this tree for a given school. Or do a few ...
• 41

Cognitive traps in very early set theory

I may be wrong, but from personal experience I think the other answers are missing a crucial point, what it is like to be taking the test itself, and how people attempt to learn material. If the ...
• 291

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 ...
• 4,438