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Doesn't this allow one to prove x=y for any x, y?

x/0 = x(1/0) = x*0 = 0, so x/0 = 0 for all x.

So x/0 = y/0.

Multiply both sides by 0: x = y.


What theorem did you use that allowed you to multiply both sides by $0$? (That theorem had conditions on it which you didn't satisfy.)

No, because x/y is just an arbitrary operation between x and y. Here you're assuming that 1/x is the inverse of x under *, but it's not.

I mean in a normal math curriculum you would define only the multiplicative inverse and then there is a separate way to define fraction, if you start out with certain rings. It is kind of surprising to me that they did a lazy definition of division.

Gambling disorder was the first behavioral addiction to be officially recognized alongside chemical dependencies; the DSM-5 reclassified gambling disorder from "impulse control disorder" to "substance-related and addictive disorders."

Every human is not addicted to something good or bad. You're abusing the definition of addiction.

It's not just brilliant, it's earth-shattering.

Please double your prices, at minimum. (And port to Linux, so I can use it. Just CLI would be great.)

Making this cross-platform is definitely a goal I wanna work on, but I lack knowledge of desktop app development on Windows and Linux.

I'm glad you think the app is cheap. Honestly I think the pricing is decent for the current set of features. I might revisit the price if I sneak in more features worthy of a higher price tag, but for now, it's good enough.


Also see physics: "quarks," "strange," "charm"


You can't expect people to express themselves freely when a single mistatement could land them in prison.


Dunn was jailed eight weeks for posting three memes:

> Prosecutor George Shelley said Dunn had posted three separate images. The first one showed a group of men, Asian in appearance, at Egremont crab fair 2025, with the caption: “Coming to a town near you.”

> The second also showed a group of men, Asian in appearance leaving a boat on to Whitehaven beach. This, said Mr Shelley, had the caption: “When it’s on your turf, then what?”

> A final image showed a group of men, again Asian in appearance, wielding knives in front of the Palace of Westminster. There was also a crying white child in a Union flag T-shirt. This was also captioned, said Mr Shelley, with the wording: “Coming to a town near you.”

https://www.newsandstar.co.uk/news/24513379.sellafield-worke...


Based on those descriptions... it sounds like he was pretty clearly racist? From the article:

> Sentencing Thompson, Judge Temperley had said of the zero tolerance approach being taken by courts:

> “This offence, I’m afraid, has to be viewed in the context of the current civil unrest up and down this country. And I’ve no doubt at all that your post is connected to that wider picture.

> “I don’t accept that your comments and the emojis that you posted were directed at the police. I’ve read in the case summary of the comments you made on arrest which clearly demonstrate to me that there was a racial element to the messaging and the posting of these emojis.

> “That has to be reflected in the sentence...there to be a deterrent element in the sentence that I impose, because this sort of behaviour has to stop.

> “It encourages others to behave in a similar way and ultimately it leads to the sorts of problems on the streets that we’ve been seeing in so many places up and down this country. This offence is serious enough for custody.”

So the actual news here is "man jailed for sharing memes that Asian people are invading the UK and coming to murder you".


Yes. It's a horrible sentiment, and he should be able to air it. Free and open discourse requires me to allow you to say things I dislike in exchange for you tolerating my saying things you dislike. It isn't free speech if you're only allowed to say popular things.


The continual conflation of speech that harms society as "speech I dislike" is absurd. And yes, it's not American-style freedom of speech... we've never had that nor should we. Just look at what American-style freedom of speech has done to America.


As a minority, I do not hold the same view. I understand your position, however, my personhood is often demonstrably conditional on the speech that other people spread about me and people like me. In the last decade I have seen fascist speech go unpunished and, consequently, the increased spread of the idea that I and people like me are not people, that I am simply an evil and horrible person for my genetic identity, forever tainted, an "undesirable", and a very suitable target for being marginalised and erased (often violently) from society. I have already been victim to these effects, as have my friends, and I have seen others, those with a different skin colour on top of the genetic difference, bear the effects tenfold. I have known of people murdered in the streets for simply having my genetic trait, even if it didn't hit the international news, I saw how people spoke about it online even despite the hate speech acts. That another one of us dead was a good thing.

I have also been witness to the power that physical violence inflicted upon these people has had in silencing that rhetoric and the spread of those ideas. I have seen how fascists go into hiding when they feel they will be the victims of violence, and I have seen how easy it is to break apart these networks by simply restricting the speech of a handful of people, or removing them from the platform.

I very much do feel, that either I am in a concentration camp in the next ten years, or these people are imprisoned. Prison is the lighter sentence for fascist rhetoric, and represent sane and sensible consequences for suggesting that an entire group of people who hold no specific ideology are evil. Remember that a war was fought, and the alternative to imprisonment for fascist rhetoric is letting it grow so large that the only inevitable solution is a war where people are murdered for their fascist rhetoric.

Before comparing the third paragraph with the first, please remember, that these people can simply choose to not say vile things about people with my genetics. If they do not wish to go to prison, maybe they should not make wide fascistic statements about people with my genetics being murderers and pedophiles — both claims that are starkly in opposition to the evidence. I am 60% more likely to be sexually assaulted compared to the baseline, cisgender female population. I cannot change my genetics, nor would I want to if I had the option, and my genetics do not represent my ideology or how I behave or act in public or private.


We know this doesn't work, and it's insane Americans still pretend it does. Goebbels himself said it while they were abusing the Weimar German freedoms and protections of democracy to take power with violence. They were very happy to use the tools of democracy to destroy it. We owe it to our societies and democracy not to let this kind of speech in particular to prosper.

And for a more recent example, you have a presidential couple that (among a million other things) lied publicly, and admitted to it. And they're now in power because their hatred-filled lies were not checked. And the country is sliding fast towards fascism, ignoring courts to concentration camps with no records to suing media to bully them into favourable reporting to pick any other example you want. Guess the country!


It's unfortunate that this seems to have been forgotten in only a few decades, but one day you may find yourself as the one who is clearly racist and despite your protests there will be no one left to defend you


Those examples are completely inoccuous to my sensibilities. Of course, there are plenty of countries that lack the broad speech protections Americans enjoy, but one doesn't expect such curtailments of personal liberty in a fellow English-speaking western "liberal" democracy.


The first example was "man arrested for wearing the exact same outfit as a man who intentionally blew himself up, killing 22 people". It's not "he was wearing the same chequered shirt!" either. As a UK citizen... I don't see how that fits under "free speech", lol

Even with "freedom of speech", you do not have "freedom from fascism" built into that, case in point, Wikipedia has multiple pages documenting both the current US administration's attitude towards trans people (that, in Charlie Kirk's words, we are "abominations unto god" that should be "taken care of" "as in the 50s/60s", which can only be taken to mean lynching), as well as the attitude of the US presidency towards democracy

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

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

https://en.wikipedia.org/wiki/Executive_Order_14290 (were PBS and NPR "biased"?)

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

https://www.theguardian.com/commentisfree/2025/sep/25/transg...


Freedom to choose clothing wouldn't fall under any version of freedom of speech?

I would would work with your fellow citizens to change that.


I think the issue here isn't "freedom of speech", its that people who claim to want "freedom for speech" are either using it as a shield to say vile things to other people, or they feel that "freedom of speech" is the only thing one needs to guard against fascism.

The resulting difficulty is that the former is demonstrably true, and the former is demonstrably false.


You can't rush enshittification.


They will just let stories die down and try again in a few more months. It is inevitable.


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