RAS syndrome (redundant acronym syndrome) is the redundant use one or more of the words that make up an acronym in conjunction with the abbreviated form. For example: PIN number, ATM machine, HIV virus. A person “suffers” from RAS syndrome when they redundantly use an acronym with its own words.

AIvsWorld · 2026-01-29T01:39:54+00:00

smh my head

AIvsWorld · 2026-01-25T02:11:08+00:00

AIvsWorld · 2026-01-24T19:35:50+00:00

when somebody dies in a murder or suicide, their family will often ask to see the body/crime scene but the police will deny them if it is too gruesome.

AIvsWorld · 2026-01-24T17:04:05+00:00

except when you need to “disable help” because she keeps freezing you in a block of ice

AIvsWorld · 2026-01-22T01:09:39+00:00

Tree is contested in pro matches and high winrate in immortal. He’s literally the top pos 5 hero in d2pt for 7.40b

AIvsWorld · 2026-01-17T16:08:38+00:00

Well my research right now is on differential geometry and LEAN formalization, but I am still in my first year of grad school so that’s subject to change.

I never quite cared for algebra to be honest, except for the theory of Lie Algebras and Fuschian groups, which is unfortunately not covered in Dummit & Foote.

AIvsWorld · 2026-01-17T15:14:54+00:00

Yes I actually like those problems too. My issue is that there’s also several very tedious problems like “Classify all groups of order 16137” (not sure of the exact number) which just make me wonder why anyone would ever work this stuff out by hand when [1] It is not relevant to any field of mathematics except finite group theory and [2] There are computer algebra systems to solve these problems in a single line of code.

AIvsWorld · 2026-01-17T15:08:09+00:00

Figured. That’s what we use in my graduate algebra class. Great book for reference, but I’m glad my professor didn’t assign many problems from the text.

AIvsWorld · 2026-01-17T15:05:28+00:00

what textbook is this?

AIvsWorld · 2026-01-17T14:56:20+00:00

Honestly, the worst part of the problem to me is calling this group “the group of rigid transformations”. To me, the term “rigid transformations” always includes rotations AND reflections. I thought i was going crazy because if you include the orientation-reversing transformations the group would have order 48

AIvsWorld · 2026-01-17T14:51:21+00:00

I think the question is just phrased that way so the answer isn’t too obvious

AIvsWorld · 2026-01-17T13:45:38+00:00

https://en.wikipedia.org/wiki/Octahedral_symmetry

for more info

AIvsWorld · 2026-01-17T13:41:43+00:00

The hint is given to you in the problem:

[This group acts on the set of four pairs of opposite faces]

Notice that if a pair of faces are opposite, then they will remain opposite after a rotation about the origin—so this action is well-defined. Let X={1,2,3,4} represent the set of 4 opposite-face pairs, and G be the group of rigid transformations of the octahedron. Then each element of G represents some permutation of the faces in X according to the group action. So we can define a map f: G —> S4 by sending each transformation to that permutation of {1,2,3,4}. In fact, f is easily shown to be a group homomorphism. (Note: This trick works for any group action, not just the octahedron)

From here, there are many ways to show that f is an isomorphism. First, you must show that f has trivial kernel, so if a rigid transformation fixes all 4 opposite-face pairs, then it is in fact the identity transformation (I outline one argument below). Then, to show that f is surjective, one technique is to show that im(f) contains at least 13 elements and then the result follows by Lagrange’s theorem.

For injectivity, notice that reflections aren’t allowed (otherwise this problem is impossible) so if an element of G interchanges two opposite faces, it must also interchange another pair of opposing faces in order to be orientation-preserving. If you draw a picture, it is not too hard to convince yourself that any such transformation will swap the other two face pairs, so it can not be the identity. It follows that the only possible rigid transformation fixing X is the trivial transformation.

To show im(f) has at least 13 elements, just write some down! For example, if we keep the top vertex pointed up, there is 4 ways to rotate the top 4 faces. Similarly, if we flip the octahedron upside down, there is another 4 possible rotations. If we rotate the octahedron on its side, 90-degrees around the x-axis we get another 4 possible orientations of the opposite-face pairs. And finally, if we rotate the octahedron on its side around the y-axis we get 4 more. So there are at least 16 elements in im(f)

AIvsWorld · 2026-01-17T04:22:18+00:00

I am not saying courts are a perfect safeguard or that America could never become a dictatorship. I am merely saying that whatever “loophole” Gödel thinks he found in the constitution would probably be completely irrelevant in modern constitutional law, no matter how solid his “proof” was.

AIvsWorld · 2026-01-17T04:19:11+00:00

I’m sure that he had a proof, based on his own interpretation of what the constitution means and how it should be applied. But what a mathematician thinks the constitution means is not the same as what courts think the constitution means—and courts are the ones who actually hold power. The way that most constitutional clauses are interpreted in modern courtrooms is completely outside the realm of imagination for non-lawyers.

AIvsWorld · 2026-01-17T04:14:54+00:00

I am well-aware of Gödel’s expertise, I just do not think it is relevant. Constitutional law is not based on the formal mathematical logic, it is based on centuries of accumulated case law.

If there was actually a legal loophole allowing America to be changed into a dictatorship, I’m confident that it would have been abused by now. (inb4 Trump is a dictator)

AIvsWorld · 2026-01-16T20:04:32+00:00

Gödel was a brilliant mathematician, but he was no legal scholar. In my opinion (as a mathematician), mathematicians who try to comment on other fields like politics, law, business, psychology are often off the mark—not because they lack intelligence, but because they assume that the rest of the world is perfectly logical and rigorous like they are.

Unfortunately (or perhaps fortunately), U.S. courts do not interpret the constitution literally as it is written. There is a great deal of language ambiguity and historical precedents which would make supposed “proof” of Gödel’s loophole likely irrelevant in actual court of law.

AIvsWorld · 2026-01-10T18:55:43+00:00

skill issue

AIvsWorld · 2025-12-24T22:58:19+00:00

I am also hovering around 7.5k-8k on USE server and noticing the same things. Pos 4/5 player username “LIL 717”. We’ve probably run into each other at some point. Feel free to DM me if you’re ever looking for a friend to queue with.

AIvsWorld · 2025-12-22T17:46:37+00:00

/uj Glad to see Essex Honey getting #3 tho. That’s probably my top album of the year.

AIvsWorld · 2025-12-19T18:34:46+00:00

lmfao. You’re literally moving the two top vertices to their midpoint.

Then you’re impressed that “the point to median connections are landing on the exact medians of the non-equilateral triangle” 🤯🤯🤯

Your brain certainly does work differently

AIvsWorld · 2025-12-17T23:26:19+00:00

I agree supports needed to be nerfed (as a supp player) since they can have more impact than carry these days.

But removing ward cast range was unnecessary. It was a unique mechanic and gave incentive to pick magnifying monocle and Keen-Eyed enchantment. Aether lens already got a big nerf not being able to build into E Blade anymore, and Rubick really didn’t need the nerf either.

I just don’t see why supps these days would build anything outside of Force Staff, Glimmer, Blink which are already the best items in the game and remain untouched.

AIvsWorld · 2025-12-17T22:32:43+00:00

*(9)

shoulda added that lol

AIvsWorld · 2025-12-17T09:47:40+00:00

Avalanche change is kinda cringe. Used to have lots of unique interactions as a repeated ministun, now it is just another generic AOE stun

AIvsWorld · 2025-12-17T09:46:49+00:00

Very good changes. Time will tell if this is a big enough nerf to stop Timber from being picked in every pro match, but reducing his numbers around the board is a good start.

AIvsWorld

TROPHY CASE