I love when a textbook has a theorem that is just the most obviously true shit, like girl I sure hope so, if that weren't true I think math would fall apart!

I especially love the conjunction of "this problem is intuitively plain as day" and "it took mathematicians centuries to formally prove this." What do you mean it takes advanced topology to prove every closed curve has an inside and outside

math wrapped

you solved 27183 equations you proved 0 of the millennium prize problems you used proof by induction 341 times you used proof by contradiction 177 times you used the pidgeon-hole principle 85 times you cried 70233 times while trying to prove the collatz conjecture you used your calculator for trivial sums that anybody should be able to do 23099 times you spent 443 hours trying to prove the collatz conjecture you had to google trigonometric identities 113 times you forgot to write the +c 56 times you said that dy/dx was a fraction 4 times you ripped 207 pages in half while trying to prove the collatz conjecture

I don't think this is possible????

Hello Ryan I am here to help. So the first step is pretty easy: Three cheeseburgers are worth 18, so each one is worth 6. If these are dollars, that's a steal!

From the second equation we get that cheeseburger plus fries-squared is five. Subtracting cheeseburger, which is six, from both sides, we get that fries-squared is negative-one. Math fans will know that there are two solutions to this; either fries are the "imaginary unit" 𝒾 or they are its negative, -𝒾. We'll do the rest of the problem with 𝒾, keeping in mind that at the end we should also take the complex conjugates as solutions.

Finally, we have that cup to the power of fries, minus cup, equals three. Replacing fries with 𝒾, and moving a cup to the other side, we get that cup-to-the-𝒾 is equal to cup-plus-three.

Now, the weird part about this is the cup-to-the-i. The problem with this is that complex exponentiation is technically not a thing. That is to say, there is no one function which is mathematically equal to "input-to-the-power-of-𝒾". In fact, there are infinitely many such functions.

Fortunately, due to reasons that take about six pages to explain (trust me I've done it), there is one particular function that many people have agreed is "the most reasonable one". This is not a mathematical notion, but a human preference. Seeing as this question was presumably written by a human, I am comfortable with using this function.

So, what function is this? Well, given a complex number r∠θ written in polar form (if you don't know what that means don't worry), where -π < θ ≤ π, then (r∠θ)^𝒾 = e^(-θ)∠ln(r).

Applying this to our problem a value r∠θ will be a possible solution for cup if e^(-θ)∠ln(r) = r∠θ + 3. Splitting this into real and imaginary parts, we get two equations: e^(-θ) cos(ln(r)) = r cos(θ) + 3 and e^(-θ) sin(ln(r)) = r sin(θ). We can graph these equations on Desmos:

The possible values of cup are the intersections between the red, green, and purple. There are infinitely many of these which have an angle of around -π/3, and there are two weirdos: One which is a complex number very close to -2.98, and one which is somewhere around -25. The possible values for cup are all of these infinitely many solutions, and also all of their complex conjugates.

They were right, 99% of people can't solve it.

this fibonacci joke is as bad as the last two you heard combined

Godelian jokes

A mathematician and a contrarian walk into a bar

Bartender: "So what'll you girls be having?" Mathematician: "The contrarian won't order anything." Contrarian: "I'll have a drink." Mathematician: "It's now obvious that she's having a drink."

The mathematician has contradicted herself. She is inconsistent.

-----

A mathematician and a contrarian walk into a bar

Bartender: "So what'll you girls be having?" Mathematician: "The contrarian will have a drink." Contrarian: *leaves* Mathematician: "She'll be back."

The contrarian never comes back. The mathematician is consistent, but unsound.

-----

A mathematician and a contrarian walk into a bar

Bartender: "So what'll you girls be having?" Contrarian: "I'll have the opposite of whatever the mathematician thinks I'll have". Bartender: "So... uh..." Mathematician: "If I'm consistent, then I won't speak for her and she won't order anything." Bartender: "Are you? Consistent, I mean?" Mathematician: "Let me have a drink while I think about it."

The mathematician never decides. She is consistent and sound, but doesn't know it. The contrarian doesn't have a drink.

---

Several hours later...

Bartender: "I'm pretty sure she's consistent. My shift is over, I'm going home."

The bartender has a higher consistency strength than the mathematician.

---

An infinite amount of time passes. An oracle walks into the bar.

Oracle: "The mathematician never decided, the contrarian never had a drink, and the Bartender was consistent too."

She speaks in an ancient and impossible tongue which nobody can understand. Everyone else is dead. The oracle is uncomputable.

A contrarian oracle walks into the bar....

The humbling ordeal of reading Mansfield Park and realising you relate to Fanny Price a little too much for comfort...

Two statements about characters can and should co-exist: Pride and Prejudice edition

Mr Bennet has a close relationship with Elizabeth and provides amusing observations on the folly of human nature BUT he is a terrible husband and father who consistently neglects the women who rely on him for absolutely everything; Elizabeth and Jane turned out so well in spite of him, not because of him.

Mrs Bennet's behaviour is understandable given the era in which she lived and the subsequent pressure she was under to get her daughters married well, which wasn't entirely for vanity reasons given that Longbourn was entailed BUT she was still fundamentally vain, ridiculous and rude; such pressure, even combined with an absent husband, still does not make her behaviour justifiable, nor her a sympathetic character, as she enabled Lydia (whose subsequent elopement with Wickham almost ruined the family) for far too long.

Mr Collins is unfairly portrayed as a middle-aged sycophant in most adaptations, rather than the young clergyman who sucks up to his patroness in pursuit of a more lucrative living that he was BUT he is still a ridiculous character who you are not meant to feel sympathy for when Elizabeth rejects him; he is rude, hypocritical and thinks of himself far too highly considering how vapid he actually is.

Caroline Bingley is often too harshly judged as a 'pick-me,' even though her relentless pursuit of Darcy is understandable given his wealth & status and how important it was for women to make a good marriage BUT she was still rude, vain and treated Jane terribly; plus she was a hypocritical snob, given the manner in which she looked down upon the Bennet family's relations despite the Bingleys' own background in trade.

Elizabeth is incredibly witty, courageous and endearing and instantly likeable which makes Darcy's slight of her at the Meryton assembly all the more of an affront to us as readers BUT, while it explains her dislike of him, she is no means perfect herself; she had far too much misplaced pride in her ability to successfully read others' characters and consequently ignored positive accounts of Darcy in favour of believing the deceitful Wickham, given her prejudice against the former.

Mr Darcy was harshly judged by Elizabeth, even though there are many more sympathetic elements to his character than immediately meet the eye BUT he was not shy or innocent; he was always a haughty rich man who had never been told no, thought far too highly of himself and, ultimately, thoroughly deserved to be rebuked and subsequently made to reform his character.

Harry & padfoot <3

we’ll we’ll we’ll if it isn’t autocorrect

okay yeah sure

I love this. I have no idea what's going on, but I love it. There's an omega with a tilde. There's at least three different kinds of space. There's the word "orthonormal". There's both set theory and integrals. There are "stochastic processes with continuous sample paths". There's all of that and this is just the if part of the if-then statement. As someone who finds incomprehensible things absolutely hilarious, this is a gold mine.

How many people are there who understand everything here? How many hours would it take to explain it to someone who doesn't understand it?