The reason that bijective functions between sets imply that those sets are of the same size is because of a generalized version of a counting argument. If a function is injective, its target must be at least as big as its source, or else there isn't enough "room" for points to map uniquely (google "Pigeonhole Principle"). For surjectivity, the target must be smaller or equal to the source because otherwise the function can't fully cover the target since the target is too big. Each point in the source can only cover one point in the target. So if a function is to meet both, the sets must be less than or equal to in size as well as greater than or equal to in size. this means that they're of the same size.

It bugged me that vim's autocomplete was giving me useless autocomplete while I was writing the draft to another blog post. So I decided to fix it, which turned out to be pretty trivial.

It comes from the Old English word for a meeting place, and the Icelandic Parliament is called the Althing (literally: 'all-thing'), and it's been around over a 1000 years, which is pretty incredible.

"As ever, if you want to find the weak point in an argument, look out for words and phrases such as"clearly","obviously", or"it is easy to see that". Often they indicate the place that the writer is not quite 100% sure about."

This post only says things that are pretty well covered elsewhere, so I'll just give my thoughts and let you look for evidence/justifications.

The iPad Pro has been marketed as a laptop replacement. I don't know anyone who thinks it can do that, at least not yet.

These are all the books in my calibre library tagged as "read". Thankfully, calibre makes it easy to get this information out of my library in a computer-friendly format.

It's odd to say this, but recently I've started reading programming language papers as a hobby. It's actually rather depressing as it's only reinforced the massive disconnect between engineering in practice and current computer science research. Isn't it frustrating to see loads of good ideas just ignored for a variety of reasons, from opaqueness to poor marketing?

Wikipedia 15 wouldn't allow me to post a long story, so here it is

Being a power user is almost always synonymous with saying you're hard to please. Which isn't necessarily wrong. I use mutt not because I like it, but because it sucks less than everything else I've used.

Sounding smart is really easy. Being smart, as far as I can tell, is the result of a hell of a lot of mental discipline.

No human has ever gotten a full mouthful of crab in one single bite. No one has ever had the pleasure of cracking a crab to only find delicious meat inside. Crab is designed so that no matter how you bite it, there is always at least one inedible bit in your mouth at any given time.

([-!#-'*+/-9=?A-Z^-~]+(\.[-!#-'*+/-9=?A-Z^-~]+)*|"([]!#-[^-~ \t]|([\t -~]))+")@[0-9A-Za-z]([0-9A-Za-z-]{0,61}[0-9A-Za-z])?(\.[0-9A-Za-z]([0-9A-Za-z-]{0,61}[0-9A-Za-z])?)+

I can't even have Markdown. Screw this, I'm moving to Jekyll or something similar. I only have static content anyway.

It's like watching a live show.

More to follow.