I used the formula N*r^d=1, assumed that N=8 and from there got r=1/16. But I can't imagine how that fractal looks like. Maybe you know an instrument to visualize or just give me a hint.
Thanks in advance!

I've come across this rather convoluted problem:

Let X be a topological space, Y a hausdorff space, and f: X -> Y continuous. Let C be a closed subset of Y, and U an open subset of X such that U contains f-1(C). If X is compact, there exists an open neighborhood V containing C such that f-1(V) is contained within U.

The question now is: Find an example where X is not compact and such neighborhood V doesn't exist.

The fact that Y is Hausdorff prevents me from using the standard pathological counterexamples with discrete and trivial topologies. I assume that Y will then be some subset of the real numbers. X is not compact, so I've tried with different open and semi-open intervals for X, but nothing seems to work.

I've tried the standard pathological functions, Thomae's function, Dirichlet's function.. I'm really not sure what to do here. Any guidance would be tremendously helpful.

Listen up. The following is the brainchild of an individual called NK, we met in a Level 2 Data Youtube stream. I am posting on their behalf. ____________________________________________________________________________________________________________

Hi r/Superstonk,

Today I am bringing a theory I would like all of you to pick apart and give your thoughts on. I have read some fantastic DD over the past year and after u/yelyah2’s post today it just… clicked. I am not bringing data, this is an explanation for the events we are seeing.

Before I present the theory, I just want to state some assumptions I am making based on available information.

1. In the years before 2020 GameStop was not doing well and COVID19 did not help. A lot of shorters saw an opportunity and went all-in.
2. I believe there is a separation between ‘shorters’ (hedge funds, family offices, banks… ) and market makers. They may be colluding, but there does not seem to be enough evidence for it.
3. However many times the float might be owned by retail, it does not matter, the events playing out signify the amount is enough.
4. There are a lot of tinfoil theories. I am ignoring them to base this theory on known, simple facts.
5. I cannot provide a timeline.
6. Although I have an economic background, this is not financial advice.

Buckle up.

Over the last weeks we have seen a lot of activities play out, including the dramatic price rise and drop over the last weeks. In my opinion, these activities are and may always have been market makers preparing to bring the necessary liquidity to the market, not necessarily to shake out retail.

Between April and August of 2020, Ryan Cohen bought a 9% (5.8 million shares) in GameStop. He upped this number to 13.9% into November 2020. I believe Mr. Cohens purchase of shares combined with the retail investors following him by buying shares and options, was enough to bring the market – the supply of GME stock - to the point of illiquidity. At the start of December, a huge delta spike was triggered during a similar price decrease as this year. As you could read in u/yelyah2’s post, it means the option market thinks the underlying (stock) is

Anyone who's ever flown in SC or ED knows that shutting down your engines while traveling doesn't bring you to a halt. Your ship just continues on its way, if you are planet side gravity will drag you to the ground post haste. But in the black - you just continue on your current vector until you hit something or explode.

Thats a problem for piracy. Right now in both ED and SC, disabling a running ship just means that you are now chasing a powerless hulk. There are creative ways to stop it. In Elite you can use cannons to slow it, but you risk blowing up the ship and the booty with it. In both games, getting ahead of the ship, gently making contact with it and slowing it down is the main way to do this.

This is unacceptable especially in SC where touching two ships together is spinning the roulette wheel on what crazy outcomes an engine under construction wants to dish out. We have tractor beams, but its already been said ship grabbing with tractor beams is risky business. Has any mention of a solution to this been given?

I know there will be many of you who say "its piracy its supposed to be hard." and you'd be correct - it IS hard, but this element transcends gameplay. You can do everything right as a pirate up to this point and have it all completely undone not by any doing of the player you're pirating, not by a mistake you made, but by the lack of tools for this type of gameplay to make sense. Thats not okay.

I tried proving this using induction, then when I looked up the proof on Google to see whether I'd missed the mark or not, a lot of the people who proved this just used contradiction or contrapositive. I wondered if my proof with induction was still valid, even if it is less simple and elegant than the contradiction proof.

Proof:

Let N_1 be a neighborhood of p. Then since p is a limit point, N_1 contains some p_1 ∈ A such that p_1 ≠ p. Further, because X is Hausdorff, there's some Z_1 of p_1 and Y_1 of p such that Z_1 ∩ Y_1 = {}. Set N_2 = Y_1 ∩ N_1. Since both Y_1 and N_1 are neighborhoods of p, then N_2 is open and contains p and thus is also a neighborhood of p, which, in particular, does not contain p_1.

Proceeding via induction, we shall assume that for all i ≥ 2, N_i = N_(i-1) ∩ Y_(i-1) is a neighborhood of p that doesn't contain p_(i-1). Clearly then, N_i contains no p_k for k ≤ i -1. Since N_i is a neighborhood of p, it contains some p_i ∈ A such that p_i ≠ p. Also, since X is Hausdorff, there's a neighborhood Z_i of p_i and Y_i of p such that Z_i ∩ Y_i = {}. Because Y_i doesn't contain p_i, then N_i ∩ Y_i is a neighborhood of p that contains no p_k for k ≤ i.

Based on this, it is clear that each N_i is a subset of N_(i-1), and so N_1 contains every N_i for i ≥ 1. Because each N_i contains a unique p_i ∈ A such that p_i ≠ p and p_i ≠ p_k for k ≤ i -1, then there are at least as many points of A in N1 as there are natural numbers, I.E., N_1 contains an infinite amount of points of A. △

What are your thoughts on this? Is it valid or do I kind of have to do this proof using contradiction? As a side note, if you have suggestions on improving my proof writing I am wide open. I tried to make this as readable as I can on Reddit. Thanks for your time!

I never used to have this problem so I do not know what has changed. I'm dreading being around other people because of this, I shower every morning, in the evening too as long as I'm not too tired, I scrub them properly with strong smelling soap, I use deodorant, clean clothes and a clean towel and for a few hours I'm fine but by the next morning I'm absolutely rank, they're sweating and honking to high heaven. Please help - I'm paranoid in public settings, I drink water every day and my diet has always been more or less the same, and this is the first time this problem has happened in years.

So, been running StK for a while now and it’s almost done. Characters just got to Neverwinter last session. One of my players who is a bit aloof about the game has consistently been writing random messages in Infernal throughout the countryside. There is no system, no motivation and honestly the messages are childish. I’m trying to run a fun, beer and pretzels type game but still semi-serious campaign. Well… the guy wrote a message in Infernal on the roof of a temple. Rolled for guards, he got caught and arrested.

Now my theory is to have a paladin present at his sentencing, accusing him of being in league with devils. Order a trial by combat, have the player lose (badly) but not be killed. Knocked unconscious then healed, the paladin stating that he has proven to be a goodly warrior through combat but still give the message that these Infernal notes need to stop.

Is that too heavy-handed?

Wondering because AGP goes hand in hand with a strong sexdrive and for me that’s something hard to handle.

View Poll

Source: https://theathletic.com/2885135/2021/10/12/amick-kyrie-irving-proves-again-hes-comfortable-being-uncomfortable/

> One thing is for sure — at least for now. While an Irving trade for Ben Simmons with Philadelphia is seen by some as an easy solution to both teams’ problems, sources with knowledge of the 76ers’ view said there is no interest in Irving at the moment. From management on down, it seems there is an unsurprising level of skepticism about that pairing working out any better than the Joel Embiid-Simmons duo that is zombified at the moment.

> And in the absence of Irving getting an extension from the Nets — which is obviously not happening now — the other tricky part here is that he can opt out of his deal after this season. That’s obviously a major factor for any interested team.

Can someone please explain the difference between a Hausdorff space and a disconnected space?

It just boggles my mind that one moment people are fully willing to talk about meat dimensions, psionics, instant regen, speed force and time manipulation, and 5 minutes later they have problems accepting that something like a 100ft. human wouldn't die instantly because of square-cube law.

"Well you can't ignore the laws of physics!"

Great, so now go into some thread about superheroes and explain how every single character breaks all of the laws of thermodynamics.

Go on, tell them how even low tier speedsters are planet tier cause they should be able to generate ungodly amounts of power just by moving.

Explain how everyone with time stop is universal cause they literally can force the entire universe to a halt.

Or how people with super strength should just sink into the ground every time they pick up something big.

Tell everybody how you can beat up Voldemort with your bare hands cause magic isn't real.

Nearly all of the who would win scenario ignore the laws of physics

You could resolve every single of the thousands Goku vs Superman threads by saying "ackshually, it's a tie cause they both turn into black holes the moment they try to attack " Pretty much all fantasy creatures have no right to exist, all of magic is founded on breaking the laws of physics, and every superpower would need elaborate secondary powers just to explain why the characters don't die every time they use it.

Like, just the sheer idea of traveling faster than light goes against everything we know about physics, a person moving at FTL speed would at the very least cause everything around them to disintegrate from the sheer force, that is if they didn't cause the reality to fucking collapse on itself or something. And people have no problem throwing FTL speed around like it's some mid tier power. But no, big animals are too much

If you can accept that Superman can get enough energy to throw planets around by sunbathing, or that Deadpool is immortal due to the power of cancer, then just accept that a giant crab would not instantly cook itself just because it's big.

Welcome back Punt Fans, to your weekly instalment of punting stats and analysis, and the best and worst clips from the last week of action as we continue our fabled hunt for the King of Punt – it’s /r/NFL’s own Punt Rank. If you haven’t been here with me before, the concept is both simple and fantastically over-engineered. Lemme break it down:

• Each punter’s performance against five vital punting metrics is ranked against every other punter in the league.
• Those rankings are combined into a weighted average ranking – the 2021 NFL Punt Rank.

Punt Heroes rise to the top; Punt Zeros sink to the bottom. Last week’s post and Week 4 standings are available here for the archivists, and this week’s update is just moments away.

I’m always excited to get your perspectives on your team’s punter, so please hit the comments below with your feedback and questions, as well as pointing out anything you think I missed.

Week 4’s shout out goes to /u/Entasis_ who correctly identified that Joseph Charlton’s Week 1 punt on 4th and 6 for the Panthers from the Jets 33 was the shortest punt attempted this year to date in terms of Available Field. And netting just 18 yards (55% of AF), you really have to wonder: why?

A hat tip must also go to /u/Moruitelda and /u/Liam90 who formed an impressive rulebook coalition to correct my misinterpretations of impetus, and very earnestly explain why Phantom Touchback was in fact correctly ruled a touchback. I mean this in the best way: if you need some dudes to get up ‘n pedantic about some shit then these are your fellas.

And now, on to Week 5!

2021 Punt Rank Standings and Week 5 Performance

2021 Punt Rank Overall Standings - Week 5

Week 5 Punt Performance Summary

Good Week for

Blake Gillikin (NO, +14 to #16). There’s a lot to process when you take over for a 12-year veteran and four time 1st Team All-Pro who was responsible for [one of the best Special Teams plays in Super Bowl history], so you can appreciate it took a few weeks for sophomore punter Blake Gillikin to settle into things. But this week… this week he looked pretty settled. Gillikin’s **five punt, 51.8

Super heavy mushroom trip had me thinking about life and the choices I was making with pharmaceuticals and liquor. While I didn’t sober up immediately after the trip, I weened off everything, sobering up almost a year or so later. Interested to hear how others realized they had a problem?

If each of the main six were represented as a topological space with the property that any two points belong to disjoint open sets, then who would get what? Bonus points for proofs that the spaces are Hausdorff.

There is a moment in Action Comics 1038 where Superman intervenes and stops the forces of Atlantis and the United States fighting over an alien artifact by confiscating that artifact and telling them because it is from off-world he will not allow it to cause conflict on Earth. Supergirl tells Superman what he did was a mistake, and when Superman asks her what she would do, she replies 'I don't know. Not that.'

Reading that sequence of panels pissed me off to such a degree that I am surprised by it. If the author wants to show within a text that the actions of a character were wrong, they need to demonstrate that there were other possible paths they could have taken. They then need to make it plausible why those other paths offered viable solutions. Alternatively, they could discuss why the rationale behind the action is flawed, and how it makes that action unworkable. Just having another character go 'You made the wrong decision', but is either unwilling or unable to provide a solution themselves, or offer a well-reasoned explanation as to why it would not resolve the problem, is horrible writing because it just leaves the audience with the impression such criticism is unfounded, and that the first character was actually justified in what they did. It also makes the character giving the criticism appear to function as a willing obstacle: they only want to block action because they do not like it and do not care about actually solving the problem. As such they weigh down and hinder the story, and do not push it forward. The only exception is when the character is intended to act as a hindrance so that they can either be horribly killed or be subject to a teaching moment, but Supergirl here is clearly meant by the writer to be in the right.

A similar portrayal occurred with the Culling of Strathholme in Warcraft 3. The town of Stratholme had its food supplies corrupted and the inhabitants were going become undead and join the enemy army. The character of Arthas decided that the residents needed to be killed to stop the whole town being turned. Arthas’ companions Jaina and Uther said his actions were wrong. However, they had no solutions themselves. They just denounced and then abandoned him. Once again, the characters acted as dead-weights.

Shitty writing leads to much infuriation.

Realized a little bit ago I may have a problem with how much Nightwish gear I own. It wasn't intentional really with what I'm wearing. It's Friday and I work from home. I wear t-shirts on Fridays. So I grabbed a Nightwish one because it was the first one I saw.

Then I like to wear necklaces. So I put on my current favorite necklace....the silver ammonite from Nightwish. I bought it as a reward for a promotion and new job.

And where my home office is by two walls of windows. It's breezy and cold. So I grab the Human Nature ruana/cape to stay snuggly warm in.

I thought if anyone is this world could appreciate this and laugh with me, it would be you all.

Anyone else have a moment of "you know you're a fan when..."?