Theorem 1. This course is awesome.
Proof: John, thanks very much for your idea of teaching this course to all of us. Having your Lectures to supplement the book has been tremendously useful; I don't think I would have understood the material if I …
Hi Eldad, John has replied to a few queries in other lectures about how to properly deal with the empty set as a special case (I don't have links to his comments at the moment). I would like a formal symbolic way of expressing the issue, but I haven…
@Charles Clingen
(You can quote a piece of text by putting > and a space before each line. It seems to work even for TeX.)
So, \( f(a \vee a') \) is indeed the least upper bound of \( f(a) \) and \( f(a') \). This implies that \( f(a) \vee f…
1) John, can you recommend a book that covers monads as a next book after Fong & Spivak (especially if it includes applications such as functional programming)?
2) I have a question that arose from trying to transfer Chapter 1's discussion of…
@Eldad Afik, that's a neat question! I wish this special case had occurred to me before, but even after trying to carefully read all the material I missed this one.
The formula for constructing \(f\) predicts that \(f(b)=\bigwedge_Q \emptyset=\top_…
Hi Christopher, thanks for the note. I'm just getting to Chapter 3 now, so I look forward to learning how all this stuff fits into the larger scheme of things!
Hi Walter, so far I've been using Microsoft Powerpoint. Unfortunately everything has to be done by hand, so no automation. I wanted to mix color and graphics, and needed to do a lot of experimentation, so I didn't try to use something like TeX (whic…
Hi David, and welcome! I used to travel to Santa Barbara often to visit a college friend who settled there; a lovely place.
I also started late and am still trying to catch up. It seems that a few people still visit the older chapters, so be sure t…
In my ongoing attempts to catch up with the class, I've just finished Chapter 2! As I did with Chapter 1, I've made a series of picture posts to help me get better intuition for the material.
The full index of picture posts is at my wiki page. If y…
Although wiring diagrams already assume associativity, I think there's a very informal way to force the concept to appear. If we want to show
[ (x \otimes y) \otimes z = x \otimes (y \otimes z), ]
we could use positional grouping to represent the …
Thanks Jonathan! I was kind of worried about including that relation. It grew into quite a large detour, and I didn't want the amount of text to discourage anyone from continuing to the last post, which is my favorite of the series.
I did want to s…
Images for understanding Chapter 1
I started the course late, and have just finished chapter 1. I've put in a bunch of work creating mnemonic images to help me understand the material, which I've just put online at my personal page here at the wiki…