#cauchy

[foolsdome]

my rendition of Augustin-Louis Cauchy (1789-1857), a prominent french mathematician, as an e-girl

[sacredwhores]

Jean-Pierre Melville - Bob le Flambeur (1956)

[freakybyte]

This is pretty similar to the solutions f: ℝ -> ℝ of Cauchy's functional equation:

f(x) + f(y) = f(x+y)

The solutions are precisely the ℚ-linear functions. These can be specified using a ℚ-Hamel basis, just like you did. Using your notation, the solutions are all of the form

f(x) = Σ a_y(x)F(y)

where F is any function from Y to ℝ. These are not rationally periodic (unless F is constantly zero), but I figured the connection was still worth a post. ^^

Hey so if a function f is periodic with period p, that means f(x)=f(x+kp) for all x∈ℝ and k∈ℤ.

Is there a term like, "rationally periodic" or something, where I could say a function f having "rational period" p means f(x)=f(x+qp) for all x∈ℝ and q∈ℚ? Is there a word for this?

[coochiequeens]

Finally a peice that talks about how 5 of the 6 in the people killed in the sydney stabbings were women. And yes he was mentally ill but he felt entitled to a girlfriend.

By Victoria Smith 16 April, 2024

Did Joel Cauchi, the man who killed six people in a Sydney shopping centre, do so because he was mentally ill? Or did he do it because he hated women?

Five out of six of Cauchi’s victims were women, which does seem targeted. Nonetheless, according to his family, Cauchi, 40, “battled with mental health issues since he was a teenager”. For this reason, some have found talk of misogyny unseemly, if not exploitative. To categorise Cauchi’s act as male violence against women, if not terrorism underpinned by misogynist ideology, can be appear dismissive of genuine sickness. Sometimes, bad things just happen because people are unwell. 

For women who live with men who have severe mental health diagnoses, there is little comfort in discussions such as these. On the one hand, there is an enormous amount of pressure to downplay the idea that mentally ill men are more likely to be violent than other men (they are, but to say so is viewed as contributing to stigma). On the other hand, is it fair for a man with severe mental illness to be judged by the same moral standards as other men? Shouldn’t we be recognising that they cannot control their perceptions and fears?

See rest of article

The Sydney attacker was desperate for a girlfriend, his family has revealed as police confirmed that he had targeted women.

Joel Cauchi killed five women and one man during a knife attack on the Bondi Junction Westfield shopping centre on Saturday.

Karen Webb, the New South Wales police commissioner, said: “The videos speak for themselves. It’s obvious the offender had focused on women and avoided the men.”

The majority of the 12 people Cauchi seriously wounded were female, including a baby girl.

Andrew Cauchi, his father, said on Monday he knew why his mentally unwell son had targeted women. The 76-year-old told reporters outside his home in Queensland: “Because he wanted a girlfriend and he’s got no social skills and he was frustrated out of his brain.”

Describing his son as “very sick”, he described trying to deal with the feelings of “loving a monster”.

A “heroic” policewoman who stopped a lone knifeman mid-rampage during a killing spree in a Sydney shopping centre has been named.

In one of several heroic attempts to disarm the attacker on Saturday, Amy Scott, a NSW Police Inspector, walked up calmly behind the attacker and ordered him to drop his weapon.

When he refused to do so and lunged at her with a knife, she shot him.

Six people were killed after the culprit – later identified by police as Queensland man Joel Cauchi – went on a stabbing spree in Westfield Bondi Junction, including a mother whose baby is reportedly now in a critical condition.

“She is certainly a hero. There is no doubt that she saved lives through her action,” Anthony Albanese, the Australian prime minister, said on Saturday.

[unconventiononthelawofthesea]

it would be easy to get confused from my posts but I am not kinky or polyamorous. I am bi tho

[errant-heron]

i can read french okay, although my vocabulary is somewhat limited. for this reason, i love having an excuse to read french monographs on mathematics, e.g. it was the only pdf i could find (honest). even Cauchy's Cours d'Analyse reads basically like 20th-century writing, and most of the technical vocabulary is of recent invention and so cognate with english

[thinkingimages]

Ben Cauchi | The Doppler Effect, 2010

Salt prints, gold and palladium toned, Framing spec: Cased portfolio consisting of matted prints + 3. 21.5 x 16.5 cm

[torschlusspanikattack]

I think it would probably suck if prayer worked bc it would be be objectively correct to spend all your time praying for yourself or others and who has time for that

[st-just]

do the qualities they'd hate thing in a separate post instead

si tu veux, I'm avoiding prepping a D&D session anyway.

Whalefall

Verity: Stupid. They're absolutely one of those people who acts a bit cynical and above-it-all to minimize the possibility of looking like a rube/says things they're really unsure of in a state of Schrodinger's Sarcasm depending on the reception. Also absolutely adores hearing gossip about other people's fuckups and bad decisions while preferring to gnaw off their arm than admit their own (serious ones, anyway). (<- one I have put the most thought into)

Yekeoul: A failure or a burden, in a fairly prosaic sense - someone who can't pull his own weight and is reliant on the charity and condescension of others. Bristles violently at anything that feels like slacking off in a way that anyone might hold against him, finds the performance of humbly begging favors mortifyingly humiliating.

Lei: Impulsive or uncontrolled. Not even so much violent specifically as just someone who doesn't have his emotions in order and can't be relied upon to keep his head and handle things sensibly and professionally.

Renata: A mark. Someone you can pull one over on or take advantage of without her ever being the wiser. She's the sort of person who gets into really impressive numbers of petty feuds but in the end can forgive just about anything except lying to her face and laughing at her behind her back.

Abhari (which I have put much less thought into the characters of)

Hira: Selfish/corrupt Iren: Foolish/imprudent Hayy: no single word, but complacent or comfortable with ignorance? Credulous of mysteries?

Valeria: possessed of delusions of grandeur? An embarrassment, someone who is humored but not respected. Jovin: A useless fop of a courtier, a relic whose time has passed Isidore: Mercenary, a man you can buy and sell

Adrien: Impious, less than perfectly devout Lionel: Dishonorable, in the sense of disgracing his inheritance and family Astrid: Ignorant, provincial, clueless of what's happening around her Dasra: Cowardly, especially in terms of superstition Patience: [answer unclear, ask again later]

[guy60660]

Ben Cauchi

[intriguingpeoplebyangelafloyd]

JOEL CAUCHI

BONDI JUNCTION WESTFIELD ATTACK

Joel Cauchi

13 April 2024

Six people (5 women and 1 man) have been murdered in a mass killing in Bondi Junction Westfield on Saturday, when at 3pm, Queensland man Joel Cauchi walked into the shopping centre wearing a green and yellow sport jersey and then left. He returned 10 minutes later and then started stabbing and killing people, mainly targeting women. There are twelve people in hospital suffering serious injuries.

            Ashlee Good was stabbed to death by Cauchi, who also stabbed her 9-month year old baby daughter who had to get emergency surgery. Australian millionaire John Singleton’s daughter, Dawn, 25, was also a victim; and there were also two victims who from overseas.

            There were many heros yesterday, including a man from Russia who tried to prevent the attacker from killing more people by fighting him off with a bollard. There were men who ran after the perpetrator, one of the them carrying a chair. One man walking behind a woman with her children (possibly his partner and children) realised the danger they were in and turned around and attempted blocking the way to protect the three. Instead of running towards the man, Cauchi dodged him and ran into a different direction.

The NSW police officer, Amy Scott, who was the only police officer on site at the time who ran towards Cauchi and shot and killed him and saved more lives in doing so.

            The perpetrator was known to police and had mental health issues. It was said that he had no police record but there are rumours online that he had been previously arrested for DV and assault - however, this is all heresay.

            There was a woman, 36, who was stabbed on Bondi Beach on Friday, 12 April - the day before the Westfield stabbings. The perpetrator of that attack hasn’t been arrested and was still under investigation when the Westfield stabbing took place. Some believe that the Bondi Beach stabbing may have been linked to Cauchi or perhaps it was just a coincidence?

            Some commenters believe he was a drug addict, we don’t know if that is true or not. One man who knew him up in QLD told the media that Cauchi owned knives which he named his ‘everyday knives’. On his Facebook account he described himself as ‘single’. He was known to go to nudist beaches, strip clubs as well as listing himself on an escort website in Sydney in June last year.

            Criminal psychologist Dr Watson-Munro stated that Cauchi ‘knew what he was doing’ and that he was ‘bad not mad’ and ‘there’s clearly planning attached to this’. He stated, “But here was somebody who was on a mission, he knew what he wanted to do and he did it with deadly affect.”

            He came down from QLD to Sydney only a month ago, rented a small storage facility and went to Bondi to learn how to surf. He went surfing at Bondi 6-days ago. In 2010, he was an online English tutor. There is still a lot of information we don’t know as yet as the investigation continues.

#2024bondijunctionstabbings #bondijunction #bondijunctionstabbings #joelcauchi #bondijunctionwestfield #westfieldbondijunction

[aorish]

looking at secondary sources for ancient greek medicine now and inevitably running into the cranks who think medicine went wrong when we stopped doing humors. like yeah it's important to recognize that ancient medical practitioners were wrong rather than stupid but this necessitates concluding that if they were alive today they wouldn't believe in any of that shit any more than actual doctors do.

[jamiesonwolf]

The Best Books of 2024!

It’s that time of year again. I can’t believe that we’re already halfway through December. I’ve gone back over the year, and it’s been filled with so many good books! I had a difficult time bring the list to just ten books, so this year it’s eleven. This year held a lot of difficult moment for me, and I wanted this list to feature the books that brought me comfort and made me forget the difficult…

[phaeton-flier]

To the Joker it's just a normal curve, as part of Straightforward Christian Economics

[floralfractals]

hi! how you doing! I'd like your help w a little something.

So I'm having real analysis in my coming sem and I'd approached my math prof about it. So I'd asked him like how do I prep myself to properly and fully understand real analysis that we'll see? like to understand it in the abstract sense and have a good intuition abt it. he suggested to try and understand the definition of real numbers and get back to him

soo uhh. I'm looking for resources to study field theory? lectures, textbooks. Any suggestions?

Thank you!

Well tbh, fields on their own are pretty tame, and as far as algebraic field theory goes, R is one of the tamest. Which is to say, a "field" just implies that you have + - × ÷ 0 1, and as long as you understand these basic arithmetic properties (as well as basic functions like sqrt, exp, log) you should be golden. Finite fields and rationals have all these crazy complicated algebraic things like field extensions and Galois theory, but R is barely interesting in that aspect.

R really shines in topology, though. For a deep understanding of the definition of R, you might want to look at some introductory point-set topology books. Key words to look out for are metric space (including the notion of open and closed sets), norm (i.e. absolute value), Hausdorff space (sometimes called T2), cardinality (of the continuum specifically), completeness.

The sources I learned these from are in my own language, so I doubt they would be of much use to you. You could internet search any of these terms though, or search for introductory point set topology books. Good luck!

[sahanmagazine]

Real numbers

Definition

A number is called a real number , if and only if it is either a rational number or an irrational number. The set of real numbers, denoted by R, canbe described as the union of the sets of rational and irrational numbers.

R = ( x : x is a rational number or an irrational number. )

R = Q ∪  “Q prime” where rational numbers ( Q ) and irrational numbers ( “Q prime” ) Subsets of real numbers

All real numbers except complex numbers are real numbers. 

Therefore, real numbers have the following five subsets :