## AC, part III: Choice in context

Wow, it’s been a long time since my last post. Sorry about that. I intend (though I’ll make no promises) to post a bit more regularly now. This final post in my ac series was advertised to be a post … Continue reading

Posted in AC, Logic, Set theory | 6 Comments

## Analysis exercise

Consider the following assertion: For any function from to the countable subsets of , there are real numbers and such that and . Can you prove it? Can you disprove it? If you can’t prove or disprove it, does your … Continue reading

Aside | Posted on | 17 Comments

Dear all: The other day I was reflecting on what material we covered in our undergrad courses, and I wondered what the most difficult proof we encountered in courses there was. Of course, we should keep in mind that every … Continue reading

Aside | Posted on | 9 Comments

## Basic AC, part 2: Choice in Algebra

The outline I (apparently) wrote on the previous post in this series says this post should talk about the Axiom of Choice in algebra, particularly how it affects vector spaces and groups. Before I talk about vector spaces and groups, … Continue reading

Posted in AC, Linear Algebra, Logic | 11 Comments

## Two neat things

Today I stumbled across two lovely bits of math(s) I’d like to share. The first is a fun topological proof that there are infinitely many prime numbers. The second is a proof that the set of prime numbers is bounded… … Continue reading

Aside | Posted on | 2 Comments

## ZN’s website

If you find yourself with absolutely nothing to do, check out my Churchill college website. There is currently almost nothing on it, but the notable thing that is there is a link to my ed Part III Commutative Algebra notes, … Continue reading

Aside | Posted on | Tagged , | 2 Comments

## Well-ordering the reals: a response

This is a reply to Jay’s comment. First, I should mention that in the absence of AC, the real numbers may not be well-orderable at all. In the Solovay model of ZF in which every set of reals is Lebesgue-measurable, … Continue reading

Aside | Posted on | 2 Comments