Seeker of Carcosa

Jarl Balgruuf energy.

Ah shit. Reading is hard sometimes.

A pint is 568ml.

Edit: the extra 30ml might be accounted for with the patented Guinness widget, a little ball of nitrogen gas that ruptures and forms a foamy head when the can is cracked.

GPT4 is wrong and it doesn’t require a price per litre comparison to prove it.

4 cans at 440ml cost £4.50. Therefore 12 cans at 440ml cost £13.50, £1.50 less than 12 cans at 330ml.

Sorry if you’ve seen this already, as your comment has just come through. The two sets are the same size, this is clear. This is because they’re both countably infinite. There isn’t such a thing as different sizes of countably infinite sets. Logic that works for finite sets (“For any finite a and b, there are twice as many integers between a and b as there are even integers between a and b, thus the set of integers is twice the set of even integers”) simply does not work for infinite sets (“The set of all integers has the same size as the set of all even integers”).

So no, it isn’t due to lack of knowledge, as we know logically that the two sets have the exact same size.

The niche story/support communities were a real staying power for me until they started taking a nosedive ~5+ years ago. Suddenly power-users were showing up, posting their creative writing exercises in all tangentially related subs, and it got ate up because over the top drama is more entertaining to some than true (or at least very plausible) stories.

It began with users policing others. You called out a fake story and you got half a dozen people playing devils advocate asking how you knew the story was fake. The poster being a serial poster who has dozens of box-ticking ragebait stories (per week) across multiple subs isn’t a clear enough indicator that this is a creative writing exercise for them.

Before long, subs were seeing much more engagement due to copycats and drama seekers; suddenly the rules prohibited calling out fake stories. Suddenly your support subreddit for offloading about your abusive parents has turned into the personal playground for creative writers with 58 part epics about their mother getting arrested for the fifteenth time for brandishing a knife at a baby at the family dinner.

I’ve already unsubbed from a community on Lemmy because I’ve seen one creative writer is cross-posting to Lemmy under the same name.

I admit the only time I’ve encountered the word utility as an algebraist is when I had to TA Linear Optimisation & Game Theory; it was in the sections of notes for the M level course that wasn’t examinable for the Bachelors students so I didn’t bother reading it. My knowledge caps out at equilibria of mixed strategies. It’s interesting to see that there’s some rigorous way of codifying user preference. I’ll have to read about it at some point.

Actually, the commenter is exactly right. The real line does contain the open interval (0,1). The open interval (0,1) has the exact same cardinality as the real numbers.

An easy map that uniquely maps a real number to a number of the interval (0,1) is the function mapping x to arctan(x)/π + 1/2. The existence of a bijection proves that the sets have the same size, despite one wholly containing the other.

The comment, like the meme, plays on the difference between common intuition and mathematical intuition.

Yes, there are infinities of larger magnitude. It’s not a simple intuitive comparison though. One might think “well there are twice as many whole numbers as even whole numbers, so the set of whole numbers is larger.” In fact they are the same size.

Two most commonly used in mathematics are countably infinite and uncountably infinite. A set is countably infinite if we can establish a one to one correspondence between the set of natural numbers (counting numbers) and that set. Examples are all whole numbers (divide by 2 if the natural number is even, add 1, divide by 2, and multiply by -1 if it’s odd) and rational numbers (this is more involved, basically you can get 2 copies of the natural numbers, associate each pair (a,b) to a rational number a/b then draw a snaking line through all the numbers to establish a correspondence with the natural numbers).

Uncountably infinite sets are just that, uncountable. It’s impossible to devise a logical and consistent way of saying “this is the first number in the set, this is the second,…) and somehow counting every single number in the set. The main example that someone would know is the real numbers, which contain all rational numbers and all irrational numbers including numbers such as e, π, Φ etc. which are not rational numbers but can either be described as solutions to rational algebraic equations (“what are the solutions to “x^2 - 2 = 0”) or as the limits of rational sequences.

Interestingly, the rational numbers are a dense subset within the real numbers. There’s some mathsy mumbo jumbo behind this statement, but a simplistic (and insufficient) argument is: pick 2 real numbers, then there exists a rational number between those two numbers. Still, despite the fact that the rationals are infinite, and dense within the reals, if it was possible to somehow place all the real numbers on a huge dartboard where every molecule of the dartboard is a number, then throwing a dart there is a 0% chance to hit a rational number and a 100% chance to hit an irrational number. This relies on more sophisticated maths techniques for measuring sets, but essentially the rationals are like a layer of inconsequential dust covering the real line.

There’s no problem at all with not understanding something, and I’d go so far as to say it’s virtuous to seek understanding. I’m talking about a certain phenomenon that is overrepresented in STEM discussions, of untrained people (who’ve probably took some internet IQ test) thinking they can hash out the subject as a function of raw brainpower. The ceiling for “natural talent” alone is actually incredibly low in any technical subject.

There’s nothing wrong with meming on a subject you’re not familiar with, in fact it’s often really funny. It’s the armchair experts in the thread trying to “umm actually…” the memer when their “experience” is a YouTube video at best.

I like this comment. It reads like a mathematician making a fun troll based on comparing rates of convergence (well, divergence considering the sets are unbounded). If you’re not a mathematician, it’s actually a really insightful comment.

So the value of the two sets isn’t some inherent characteristic of the two sets. It is a function which we apply to the sets. Both sets are a collection of bills. To the set of singles we assign one value function: “let the value of this set be $1 times the number of bills in this set.” To the set of hundreds we assign a second value function: “let the value of this set be $100 times the number of bills in this set.”

Now, if we compare the value restricted to two finite subsets (set within a set) of the same size, the subset of hundreds is valued at 100 times the subset of singles.

Comparing the infinite set of bills with the infinite set of 100s, there is no such difference in values. Since the two sets have unbounded size (i.e. if we pick any number N no matter how large, the size of these sets is larger) then naturally, any positive value function applied to these sets yields an unbounded number, no mater how large the value function is on the hundreds “I decide by fiat that a hundred dollar bill is worth $1million” and how small the value function is on the singles “I decide by fiat that a single is worth one millionth of a cent.”

In overly simplified (and only slightly wrong) terms, it’s because the sizes of the sets are so incalculably large compared to any positive value function, that these numbers just get absorbed by the larger number without perceivably changing anything.

The weight question is actually really good. You’ve essentially stumbled upon a comparison tool which is comparing the rates of convergence. As I said previously, comparing the value of two finite subsets of bills of the same size, we see that the value of the subset of hundreds is 100 times that of the subset of singles. This is a repeatable phenomenon no matter what size of finite set we choose. By making a long list of set sizes and values “one single is worth $1, 2 singles are worth $2,…” we can define a series which we can actually use for comparison reasons. Note that the next term in the series of hundreds always increases at a rate of 100 times that of the series of singles. Using analysis techniques, we conclude that the set of hundreds is approaching its (unbounded) limit at 100 times the rate of the singles.

The reason we cannot make such comparisons for the unbounded sets is that they’re unbounded. What is the weight of an unbounded number of hundreds? What is the weight of an unbounded number of collections of 100x singles?

In short, yes.

This kind of thread is why I duck out of casual maths discussions as a maths PhD.

The two sets have the same value, that is the value of both sets is unbounded. The set of 100s approaches that value 100 times quicker than the set of singles. Completely intuitive to someone who’s taken first year undergraduate logic and calculus courses. Completely unintuitive to the lay person, and 100 lay people can come up with 100 different wrong conclusions based on incorrect rationalisations of the statement.

I’ve made an effort to just not participate since back when people were arguing Rick and Morty infinite universe bollocks. “Infinite universes means there are an infinite number of identical universes” really boils my blood.

It’s why I just say “algebra” when asked what I do. Even explaining my research (representation theory) to a tangentially related person, like a mathematical physicist, just ends in tedious non-discussion based on an incorrect framing of my work through their lens of understanding.

I’m going to use smaller words so you can keep up: I understand the point of the meme. I understand that people are having fun. I’m having my own fun in poking at the one moron who’s coming to a fun thread with actual Tory arguments and getting tilted when he gets called out.

No, a 90 year old should not be forced to work to help their family. No, there isn’t a logical argument in favour of it. You’re just making Tory arguments, and I’m poking fun at you.

I’m not missing the point at all, actually. You may notice I’m not up and down this thread shooting down everyone calling him a coke fingered nonce because that’s comical. What isn’t comical is your particular overanalysis which is outright wrong. A joking comment that he’s a workshy scrounger is a funny over-exaggeration. An analysis of how a 90 year old should be grafting to put food on the table is neither funny or correct.

And if he really is the most fragile, why aren’t the others helping out around the house at the very least so Mum can go work, rather than dedicate her life caring for an entire double bed’s worth of old people on top of her family living on one person’s wage?

I really don’t know, lad. Why don’t you dig up Roald and ask why his lighthearted kids book doesn’t stand up to your overanalysis? He’s not up to much; he’s just been grave-ridden for 30 years.

Damn, you really throwing the word Tory around like that

If it walks like a Tory, talks like a Tory, and regurgitates bootstraps rhetoric like a Tory…

Everyone from a poor or working class family understands that poverty isn’t something you can graft your way out of. Also, a man described as “96 and a half” and the most fragile among Charlie’s grandparents, managed to muster the energy to celebrate his grandson winning a prize and then accompanied him on a half day tour round a local factory. If you think that’s sufficient to classify him as work capable, then you’ve got a bright future conducting disability assessments for the DWP.

You do understand that the film isn’t a documentary? It’s a family film. You’d be the guy complaining that in episode 2F09, when Itchy plays Scratchy’s skeleton as a xylophone, he strikes the same rib in succession yet produces two clearly different notes.

Edit: Actually, there’s a lot more to say. Your comment is simply wrong on every point it makes.

Firstly, you mischaracterise the elderly, maybe from a myopic view based on personal anecdotes. People who live active lives before retirement tend to live relatively active lives after retirement. The reason they may choose to live more cautious lifestyles is because mundane injuries for a young person can spell a death sentence for the elderly. In over 65s, a simple fall can lead to a hip fracture, which has a one-year mortality rate of 21% if the patient undergoes surgery; this mortality rate rises to 70% if they do not undergo surgery.

Secondly, if you earnestly believe that a 90 year old, over 20 years into retirement, needs to polish their work boots, get on their bike, and find work to support their family, then you’re either mentally deficient, a child with zero experience of the job market, or a tory. Either way, you’re detached from reality. Forgetting the fact that a retiree has earned their retirement, a company is simply less likely to take on an over 65, either through some judgment of their ability or out of fear that a common workplace slip can turn into a death.

You really need to get some perspective on how the world works, and maybe a hobby that isn’t making ill-informed ultra-literalised criticisms of family films. Next you’ll be saying that Grandpa Joe should learn to code so he can remote hustle from his bed.

It’s not a necessary tool for all fields. I don’t know your area but mathematics journals have vastly different style guides and citation standards. The best way to handle this is to export a bibtex citation which is just a list of metadata tags, then plug in the journal’s style header before compiling your TeX.

That’s because mathematicians use log for the natural logarithm. Log base 10 would be log_10