Viewing profile — ionfish

Here is the cartoon Knuth refers to. http://www.danzigercartoons.com/archive/cmp/2002/danziger141...

I wouldn't confuse modules with modularity. Think of it like this: types are the primary API for the program. In fact, I tend to call the modules that perform this function in my c…

It's pretty common in the UK these days.

No, the default backend is the native code generator. You need to use the -fllvm flag to enable the LLVM backend. http://www.haskell.org/ghc/docs/7.6.1/html/users_guide/code-... "[…

Coming from a set-theoretic perspective, I suppose I've got so used to Tarski's theorem that I consider it intuitive. As far as Tychonoff's theorem goes, you might find this paper …

Lots. For example, that every set has a cardinality (is bijective with some aleph). That's pretty intuitive, too, as (I think) are the following. * Let X and Y be sets. Then either…

Having written the following, I now wonder whether you meant something more specific by computation than I did, so I'm not certain whether my point is really a response. Could you …

I don't care that nobody cares. I care that they pretend that they do. Fake friendliness is annoying, and good service is not formulaic.

AC is equivalent to a lot of things. There's a collection of them on the Wikipedia page. http://en.wikipedia.org/wiki/Axiom_of_choice#Equivalents Something I find pretty interestin…

The history of the proof is a little messy; the Wikipedia page has a decent summary. http://en.wikipedia.org/wiki/Cantor–Bernstein–Schroeder_theo...

Yes, it does rely implicitly on Cantor–Schröder–Bernstein. That might be a downside, but I think when working informally (that is to say, when not teaching a set theory course) one…

I think this becomes much more intuitive once one understands that the cardinality of any nondegenerate closed interval is the same as the cardinality of the continuum.

The usual way this is done is by selecting a canonical representation for the reals in the list. It's pretty much the same thing as you said, but I don't think you're putting it in…

Like I said in my response to pndmnm, in my view if someone "[would] think that the cardinals also formed a set with an (infinite) cardinality of its own" then they haven't really …

I'm not saying it's not interesting—in fact, I think it's fascinating—but all of this is implicit in Cantor's Theorem. "Harder question" to me implies there's something there that …

That's a really nice way to show that, thanks. I may borrow it for future use.

Why is that a harder question? It's a direct corollary of Cantor's Theorem that there is no largest cardinal number (assuming the powerset axiom, of course).

The set of fractions isn't larger than the set of whole numbers, so how good an explanation could it be?

I don't think one can ignore that and also focus on practicality. Using these JS dialects is a practical issue. Learning them and remembering how they work imposes a certain amount…

> having to write Udon.curry everywhere sort of takes away from that cleanliness you are trying to recreate. This is true, and I considered your approach when writing functions lik…

You probably shouldn't. :)

Oh, I think it was mainly trivial stuff. I'm afraid I don't remember the specifics, this was two years ago.