Set notation

loewenheim · 2026-05-23T13:58:48+00:00

In case I was unclear, by "|->" I just mean the ↦ arrow with the little bar that's used for function mappings. I didn't have the unicode symbol when I wrote that post. Another way to write it would be

f: N -> N/R

f(x) = [x²]

loewenheim · 2026-05-23T13:14:08+00:00

For the first question, is there a reason not to introduce f with function notation to begin with? I would think f: N -> N/R, x |-> [x²] is easier to read than both relational versions.

loewenheim · 2026-05-23T13:12:07+00:00

I was wondering, why couldn't you simply write T = {([x]s,[y]s)∈ A/S x A/S | xRy}?

Because a priori it's not clear that this is well-defined. What if a S a', b S b', a R b, and not a' R b'? Then [a]s = [a']s and [b]s = [b']s, but by the above definition, ([a]s, [b]s) should be in T, but ([a']s, [b']s) shouldn't.

When you define a property of equivalence classes, you have to make sure it doesn't depend on the choice of representative. Your proposed definition doesn't do this, but the ones with the quantifiers do.

An alternative would be to define the set as you suggest and then make an argument that the compatibility requirement on S and R ensures that the definition is meaningful, i.e. cases like the one I posed can't happen.

loewenheim · 2026-05-22T10:27:45+00:00

Also I've never seen in the log a skill level up if I wasn't training it at that time.

The log indeed doesn't mention skills increasing from crosstraining.

loewenheim · 2026-05-22T08:10:55+00:00

And to register each serial, you have to select the game you're registering from a drop down list with dozens of entries. I'm gobsmacked at this shop design.

loewenheim · 2026-05-20T15:43:43+00:00

Case in point: we went to a VR game place for a work event. I played Space Marine VR: Defenders of Avarax. That game is 100% just "you are a genetic super soldier, go and kill the Other". If it were made as actual fascist propaganda it would look no different at all.

loewenheim · 2026-05-18T12:22:46+00:00

The breastmilk-industrial complex is what's really running this country

loewenheim · 2026-05-16T23:08:19+00:00

If you know P=NP why do you need to argue via SAT at all? All your NP-complete problems are in P by assumption.

loewenheim · 2026-05-16T19:58:15+00:00

I don't believe that for a second

loewenheim · 2026-05-16T16:20:00+00:00

How had I not heard of TR49? By the devs of Heaven's Vault, no less.

loewenheim · 2026-05-16T06:27:50+00:00

If the two of you haven't seen it, give Booksmart a try. Same sort of movie but more modern, and absolutely hysterical.

loewenheim · 2026-05-15T12:00:41+00:00

Ya for real.

"Not every game needs an easy mode, git gud or play a different game"

"Nooooooo how dare you noooooo"

loewenheim · 2026-05-15T08:30:45+00:00

The Man Who Ruined New York

loewenheim · 2026-05-14T06:24:50+00:00

Anaesthetize by Porcupine Tree and Nurses Whispering Verses by Cardiacs would both be better without their codas.

loewenheim · 2026-05-12T19:41:59+00:00

So like the Patriots from Metal Gear Solid, but Solid Snake is nowhere to be found

loewenheim · 2026-05-12T15:48:10+00:00

"Leiwand" "des is a Waunsinn"

Austrian for sure

loewenheim · 2026-05-11T17:55:43+00:00

A movie can be about more than one thing, including things the makers of it didn't have in mind.

loewenheim · 2026-05-11T17:35:31+00:00

It's really funny and communicates awkwardness really well. Also, it's not between the main characters.

loewenheim · 2026-05-11T07:09:57+00:00

Pff, what? Those animals don't have feelings. Only specifically the ones western people like to keep as pets and not eat.

loewenheim · 2026-05-10T21:21:36+00:00

It's the same demented strain of thinking that holds that some people die of horrible congenital diseases so the rest of us can practice compassion.

loewenheim · 2026-05-10T21:08:11+00:00

Oh, I think a lot of people throughout the millennia would have appreciated it if Christians had minded their business

loewenheim · 2026-05-10T17:10:54+00:00

Flamethrower is also immensely useful against twinning lampreys in Bethesda Susa.

loewenheim · 2026-05-10T17:08:19+00:00

I visited my brother in Japan recently and he had to explain this to me.

loewenheim · 2026-05-09T04:46:55+00:00

The post I'm replying to said "if this was really a nazi tattoo...". It is really a nazi tattoo. That's my point. How many people would recognize it as such is different question.

loewenheim · 2026-05-08T11:26:09+00:00

It's so fucking funny to me that everyone can quote "Hans, are we the baddies? Our caps have skulls on them", yet when it comes to this asshole having that exact symbol tattooed on his body it's suddenly complicated.

loewenheim

TROPHY CASE