Aren’t infinite universes technically impossible because there would be infinite possibilities which would mean in one of those possibilities a universe that has complex intelligence been able to travel through universes and go see us? Also if there is infinite universes with infinite possibilities if there were to be one possibility there would be an infinite amount of that possibility.

Or suggestions on the history of set theory in general? Thank you!

https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-20170912/

Question comes from reading this article. I am an undergrad math major who has not really delved into set theory yet. I was hoping someone could illuminate this subject or give me some intuition about it. Is it that it could be proved using some other “better” axioms?

I need to know what this is for a math project. I have searched around the web and haven't come across a simple explanation. Help! :)

Amateur mathematician here. I have read about formal logic and axiomatic systems and have encountered several axiomatic systems that have been proposed to "explain" all of mathematics. We are all familiar with Whitehead and Russell's Principia Mathematica, Zermelo-Fraenkel Set Theory, Peano Arithmetic, Lambda Calculus, and Second Order Arithmetic. Each of these systems attempts to form the basis of mathematics, but which one is truly the basis for mathematics? Are there any noticeable differences between them? Does it even matter whether which axiomatic system forms the basis for math? Although I have seen literature that cites ZFC as the basis, many other sources also use Peano Arithmetic or Second Order Arithmetic, especially for formal logic.

A simple example would be the [Axiom of Union] (https://en.m.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory#5._Axiom_of_union):

We have a small basket with an apple and a banana and another small basket with a banana and an orange. Both small baskets we put into a bigger basket. Now we can say that the bigger basket contains apple, banana and orange.

If we could demonstrate all axioms in a similar manner, would that be sufficient to prove that humans did not invent mathematics but rather discovered it?

I'm looking for an English translation of Zermelo's 1913 paper on the existence of an optimal strategy for Chess, Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels. Searching the web, I found the German original but no English translation.

Wikipedia entry on Game Theory: "In 1913, Ernst Zermelo published Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels (On an Application of Set Theory to the Theory of the Game of Chess). It proved that the optimal chess strategy is strictly determined. This paved the way for more general theorems."

EDIT: If no English translation of the original paper exists, I'm interested in producing one. Until a translation is found or produced, the following documents may be of interest to this subreddit:

Description of Zermelo's paper & the mathematics of chess from St. Andrew's

Original German version of Zermelo's paper

Zermelo and the Early History of Game Theory

I know a relatively ok amount of math (calc III, diff eq's, linear algebra). I've heard that ZFT and the Axiom of Choice provide a basis for mathematics. I don't get how a framework involving sets can lead to (or provide a foundation for) numbers, addition, multiplication, functions, etc... Any help?

The news is all over the board, but just in case you're crawling out from under a rock...

THE BACKSTORY:

On June 1st, news broke that Mudrick Capital purchased 8.5M shares of AMC common stock, netting AMC almost a quarter of a billion dollars. Mudrick turned around and sold their ENTIRE STAKE that afternoon under the pretense that AMC was "overvalued".

THE THEORY:

The 8.5M shares were a trap set by Adam Aron for none other than Citadel to expose their connection to Murdrick, thereby pivoting the story from “bearish sell off” into an opportunity for Apes to shine.

(Edited the theory for clarity.)

THE ASSUMPTIONS

With an average share price of $27.12, the sale would have had to pre-date the day's pre-market. It is likely the shares were purchased heading into the close and after hours on Friday.

I can only imagine that, in a sale of this size, and based on his defense of the sale this morning on Twitter, Adam Aron was directly involved.

It also strikes me as reasonable that the executive team at AMC did their own DD on the buyer.

THE FACTS

According to Fintel, Ken Griffin is listed as fund manager: https://fintel.io/so/us/mudsu/citadel-advisors-llc

AMC has a total of 524,173,013 shares authorized, but as of the completion of the at-the-market offering, AMC had 450M outstanding shares and “free float” of 447M. This means AMC had, roughly 70M shares with which to sell as of last Friday.

PUTTING IT TOGETHER

Think about this. It's a Friday before a holiday weekend and the phone rings. "We want to negotiate the purchase of 8.5M common stock shares." AMC has 70M available, so, at a negotiated share price of $27.12, this phone call earns AMC $230.5M in cash.

Remember our assumptions. They don't immediately say yes. Someone looks up this Mudrick. They see what I showed you. Ken Griffin listed as manager.

Now, you could argue that they didn't know and proceeded anyway. But, I'm not sure that line of argument holds any water. These are business people. They dot every i and cross every t. Lawyers, I'm certain, get involved.

So, they knew.

Now, why would you approve the sale of shares to a fund connected to Citadel unless you intended to offer them just enough rope to hang themselves?

Adam Aron, has, on multiple occasions, stated that he works for the shareholders and that we own the majority of the float. He also is aware of how much effort we put into being thoughtful shareholders. He knows we research to find answers to our q

TL;DR: The Eternals film will set them up to be the major antagonists of phase 4 or 5. I have also TL;DR'd each chapter just in case someone wants to read the individual parts of the theory without reading the whole thing.

Hi, everyone. This theory comes out of a discussion my friend and I had in our weekly Loki episode discussion (which we've been having since the MCU shows have come out). With an episode with fewer in-depth details to go into, the conversation shifted into kind of the meta-discussion of the MCU as a whole which is one of my favorite topics. In my opinion, right now is the best time to kind of explore this space because we're in a weird spot where we know so much yet we really know so little. More projects and casting than ever before have been announced, but we have so few trailers to comb through and so many stories are nicely wrapped up at the end of Endgame. So this theory has a few caveats.

[Caveats]

1. The theory is mostly metatextual. Because we don't really have much in-MCU material to base Eternals theories off of, this theory is based mostly off of the meta-narrative and ideas of where the Avengers as an entity and as a team could likely go story-wise as well as the meta-narrative we can build off of announced shows and movies.

2. I am not knowledgeable at all about the Eternals. I will probably get into this later, but I feel like we are at a point in the MCU that they are pulling from source material and characters that Feige and Co. would deem "less favorable for adaptation," so I feel that the further we get into the MCU at this point the more that they are going to adapt the characters to what they need rather than adapt the MCU to facilitate the characters they want to bring in.

3. I am assuming that the marketing strategy Marvel is taking by announcing a lot of projects but only marketing projects in the EXTREME near future is a) purposeful and b) not a byproduct of Covid-19 and rather a deliberate strategy that Marvel would have followed anyways.

4. Metanarrative is a word I may or may not have made up (it doesn't have a red squiggly under it) and I am using it to mean both the overarching narrative of the MCU. I might accidentally slip and use it to mean the narrative created by casting, leaks, marketing, etc., but I don't think that's really too separate from what I'm meaning.

5. Sorry this is really long, I'm really into this theory and, though I feel like it makes perfect sense to me, I'm really rooting for it

Edit - Thanks for all your input! I've made a follow up post on the matter! -

04/11/2021 - The Fake Squeeze... Continued

___________________________________________________________________________________________________

Quick Edit - I should've mentioned the biggest point of all...

JUST BECAUSE THEY MIGHT TRY THIS, DOESN'T MEAN THEY WILL BE SUCCESSFUL! WE AIN'T FUCKING LEAVING!

We have to believe they'll try absolutely anything at this point.

__________________________________________________________________________________________________________________________

Edit - Okay, so let me clarify a few things!

• I think that highlighting a potential ‘fake run up’ will HELP people HODL even more! The biggest test for some people will be to take profits at $1000, with MSM pushing that the squeeze is finally over.

Surely providing some DD about how it is NOT REAL will HELP people HODL through it, rather than paper hand?

• Also, one major flaw in my post was the lack of accountancy for FOMO. This is a very real thing and would create heaps of buying pressure, screwing their plan altogether. It is a dangerous play for sure. I’d like to paste a comment I made below to some of the concerns.

Thanks for your comment! Let me just address some of things you've said and we can discuss.

As I've explained, major HFs could have shorted long holdings of smaller HFs. When they liquidate, not only does it not affect them (much), but they're actually profiting.

1. Very risky indeed, but when the inevitable squeeze is going to happen wouldn't you try everything possible to mitigate it?
2. Long whales only stock is not in GME. When these HFs liquidate, many of long whales other positions are going to be negatively affected.
3. Please remember not everyone who owns GME is an ape. There are people who have no idea of the fuckery afoot.
4. FOMO is the reason its a risky play.

• *'*The buying pressure could be too much'. **Well if the buying pressure is from HFs this time, there's a lot more room for fuckery. As Melvin stated before, the january squeeze was not shorts covering, more retail inve

I've looked into 4-5 different set theory books and I'm puzzled by the fact that there's a disagreement into which axioms actually constitute the ZFC axiomatic set theory?

Digging a bit further into the subject it seems that wolfram alpha has the same conclusion (i.e. towards the end, reading the last paragraphs)

http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

Which made me ask the following questions

1. Why such a disagreement, I thought math was built on solid foundations, it seems like folks can't agree on which ones to include in textbooks, how are we supposed to know which to learn/teach to students?

2. During reading these notes https://drive.google.com/file/d/1nchF1fRGSY3R3rP1QmjUg7fe28tAS428/view

it seems that the lecturer defines separately axioms of epsilon-minimal relation and the axiom of foundation, but aren't those the same thing?

From reading the above-linked wolfram page they define the axiom of f***oundation/regularity/epsilon-minimal relation*** to be one axiom, but in the notes presented above they are presented as separate axioms, is that correct? (unless if I understood something wrong)

I have found a way of proving one of the millenium prize problems using a slightly modified version of set theory.

Yang Mills is a very important theoretical problem in mathematical physics. It is needed for our modern formulation of quantum field theories among other things. According to Wikipedia, the statement of the problem is as follows:

>Prove that for any compact simple gauge group G, a non-trivial Yang-Mills theory exists on ℝ⁴ and has a mass gap Δ>0.

Let's get into the proof

All modern set theory is based on the Zermelo-Fraenkel axioms. One fundamental property of these axioma is that they guarantee the existence of a set. If we throw away this assumption, we get a theory that does not allow for sets. If all gauge groups are sets, this means we cannot construct gauge groups, hence Yang-Mills becomes trivial.

Where's my million dollars?

This is a theory about the setting of the Foxhole universe which I have tossed around as a joke before. I'm now sharing it with reddit for your enjoyment.

The core concept is that the Foxhole universe does not take place in some war-torn alternate universe. Foxhole actually takes place in the far future, where numerous players are taking place in a "full-impact" Live Action Role Play.

In this far future, humanity has defeated death through mind uploading and cloning. Scarcity is a thing of the past, as nanomachines can fabricate anything you could possibly desire and more using only raw elements. Anything from dirt to seawater can be feedstock for these nanomachine fabricators.

Without the need to worry about working for survival, humanity pushes the boundaries of its recreational pursuits. LARP is more than just foam swords; with the ability to resurrect instantly in a cloned body, humanity can engage in role-playing with fully functional weapons. Foxhole takes place in one such LARP. The players are real human beings, but unconstrained by death.

This explains many things about the Foxhole universe:

• Salvage, Components, and Sulfur are especially rich feedstock for the nanomachine fabricators in Refineries, and per LARP rules are the only raw materials that may be processed. This is why junk can be turned into what appear to be steel beams.
• Materials (Basic, Refined, Explosive, etc.) are fully processed raw materials for nanomachine fabricators found in Factories and Garages. These contain all the necessary elements to fabricate anything available in the factories.
• Stockpiles at bases do not actually contain items. Instead, bases have very fast nanomachine fabricators. The contents of the stockpile are actually the raw materials necessary to fabricate the items, and in the correct ratios. The LARP game mechanics prevent using materials earmarked for one item to fabricate a different item.
• Crates do not actually contain the item inside them. Instead, they are self-contained material packages which include the correct precursors, elements, and instructions for the smaller nano-forges found in bases. This is why you can fit more items in a crate than you can in an equivalent inventory slot; it’s just a block of special raw materials.
• Likewise with vehicle crates, which contain the necessary raw materials for a larger nano-forge at Storage Depots to produce the listed vehicle.
• Each spawn point contains a cloning machine, which can use the same

The Mistfits' attendance at Gowpenny is clearly a big deal. Everyone knows about them and they are being watched carefully as the former mug-, excuse me, namps interact with the wizarding world for the first time.

We don't have any insight yet into why these four teens were selected to attend Gowpenny Academy. None of them applied to the school, and it seems that, if anything, their selection was random. However, the one thing they have in common is that they all have pretty significant flaws for students attending a school for magic.

Whitney puts more focus on sports than academics, Dream actively wants to be an evil witch, Sam is a narcissist with a D average (Ds get degrees!), and Evan is well... Evan. I love this season's PCs, but whoever selected these four students for the exchange program clearly didn't choose them because they were the best and brightest.

We also know that the wizarding world is trying to be more accepting of non-magical people, as evidenced by the m-word recently being considered a slur. As pointed out in the episode, why would the wizards care about using a slur if the people it is being used against aren't even aware that it exists? Unless the wizarding world is planning to reveal its existence to the larger world and the Misfits are a trial run to see how namps will handle themselves.

My guess is that a witch supremacist who doesn't want wizards and namps to commingle (see Voldemort/Grindelwald), interfered with the Exchange Student selection program specifically to pick namps that would reflect poorly on the non-magical population at large. In the first episode, Dream even talks about how it's wrong to make assumptions about a large population based on the behavior of an individual.

So far, the most likely candidate behind this sabotage would be Boudicca Philtrum. As the Headmistress, she would have the most control over the selection process. This also fits in with Tallulah, Fergus, and Digsby being inversions of Hermione, Ron, and Harry, making Boudicca an evil version of Dumbledore. However, it's still early and I think it's more likely to be a character we haven't met yet.

The misfits will overcome their flaws by working together, defying the odds to prove to wizards that namps are just as capable as magic users. They may have been chosen to fail, but as the title of the first episode tells us, that still makes them The Chosen Ones.

I know the series is designed to not be set in any particular time period due to the steampunk style it has, but I’ve always wondered if we could pinpoint at least a decade when it most likely took place.

My theory is that it took place during the 1960’s or, more likely, the 1970’s. Firstly, in Eternal Diva’s opening, there’s a shot that shows the whole of London, however, the London Eye, a famous London landmark, is nowhere to be seen. Construction on it began in the 90’s so it couldn’t have set in the 90’s or the 21st century. Next, I believe some characters throughout the series refer to England having a Queen. There’s no way it’s Elizabeth I not Victoria due to the technology, so they must be referring to Elizabeth II, so the series must be set in the 20th century. The series is filled with colour TV’s, cars, airships, deasel trains, modern cruise ships, aeroplanes and references to electric guitars. These place the series sometime after the 60’s as this is when all these technologies were long invented. Finally, the image that got me to conclude that the series is set in the 70’s was the box art/promotional art for Lost Future where Layton and Luke look at the clock shop’s time machine. If you see the year counter beneath the clock, the last two numbers are in between 70 and 80. Which means that the series must be set in the 70’s and in Lost Future they travel to the 80’s.

Gimme your thoughts on this and whether you agree or not. I’m actually kinda proud of this tbh.

This has an application for something I'm working on. I imagine the answer is no since the cardinal numbers cannot be put into a set, but I can't think of an argument.

I've noticed a certain type of commenter over the last few years and I'm curious if anyone has any insight into it. I think of these people as "joyless experts."

The joyless expert is absolutely an expert in their subject domain. They know their stuff, and they aren't afraid to brandish it. However, they seem to take no pleasure in their knowledge. Rather than joining conversations in which they can say "that's a great question, let me give you some insight into it" they join conversations in which they can say "that's a dumb question and you annoy me" or "that's a dumb opinion and you annoy me" or just express a general sense of disdain toward nonexperts.

Now, I don't want to say that those non-plussed attitudes are never welcome or warranted. I enjoy a good troll smackdown as much as the next person. So maybe it'll help if I give some examples.

There was a joyless expert a few years ago on the mathematics subreddit who seemed mostly interested in beefing with people who accepted the Zermelo-Fraenkel axioms of set theory wholesale. And this wasn't the usual axiom of choice dithering. Her attitude was more like, you fucking idiots don't actually believe in the power set axiom, do you? (Later her contempt pivoted toward unrestricted comprehension, if I recall correctly.) She was abrasive and uncharitable in her interactions and so what could have been interesting conversations were unpleasant and, well, joyless.

Similarly, there was a commenter on the poetry subreddit who definitely knew her theory but mostly commented to say how people who enjoyed rhyme and meter (not even preferred, just enjoyed as a possible contemporary flavor) were basically harmful to not only poetry, but society as well. She sometimes agreed with other commenters talking about the pleasure they took in contemporary (free verse) poetry, but she was oddly disfluent in appreciation. Her positive comments were along the lines of "yes, this!" but her negative comments unspooled with sentences of vitriol.

I've encountered others too, but I'm sure you get my point.

How do these people come about? How does someone get to the point where they still want to contribute to a conversation but all they have to offer is disdain or contempt?

I'll probably sound naive or pollyannaish here, but every time I've gained some expertise in a subject I'v

I think that the Mini-set will probably be announced on 1st of June, and well, you people maybe ask me why?Well let me show my case:

1: The Darkmoon Races Mini-set was announced on 19th of January, also known as the 63th day since 17th of November, which is the day of release of Madness at the Darkmoon Faire, 1/19 was on a Tuesday.

2: Today, (when I'm writing this) 25th of May, is the 56th day since Barrens release(3/30), and the 63th day of expansion by my calculations is 1st of June, which is also a Tuesday!

But, I could easily be wrong, After all, Blizzard can be very Schematic sometimes but not always, yet I not going to leave that hope since it makes so much sense in my opinion. (Sorry for any Typos, English is not my Native Language and i not that good at writing it)

I and many others had a suspicions from the start that the Time Keepers don’t actually exist and there’s someone else pulling the strings. My gut feeling is that that someone is Loki himself.

We’ve still yet to see who Richard E. Grant is playing and one of the more popular theories is that he’s likely playing an older Loki variant. I think this as well but I think they might also be combining him with He Who Remains.

He Who Remains is a pretty obscure character but he was the final director of the TVA and was responsible for creating the Time Keepers. (He also created the “Time Twisters” which are the name of a weapon the TVA uses in the show I believe, so that’s a cool little easter egg) His first appearance was in a Thor comic as well.

My thoughts are that Old Man Loki created the idea of the Time Keepers for whatever purpose and is actually the power behind the TVA. Somewhat similar to what we saw Loki doing with Odin In TWD and Ragnorok.

The MCU likes amalgamates characters sometimes, Sylvie herself is a combination of Lady Loki and Sylvie Lushton, and/or give characters traits or story beats similar to another. So it wouldn’t be too far out of the realms of possibility that we could see something similar.

Considering Loki’s use of illusions and trickery and the multiple versions of him we’ve already seen, l think having an older Loki secretly pulling the strings and being the “man behind the curtain” and using the Time Keepers as a smoke screen for his ultimate goals would make a lot of sense.

I fully admit could be totally wrong and I’m willingly to throw my hands up if I am. This is just me rambling about the thoughts I’ve been having about the series, I always find fan theories to be fun (within reason obviously).

I’m not going to be too torn up if my theory turns out to be wrong, as long as I keep enjoying the show like I already have been then I’m happy.

TL;DR: The Time Keepers don’t exist and are personas created by an Old Man Loki variant that is actually the one in control of the TVA.