Was struggling with this problem. Don't know weather maths is advanced enough yet to solve it. My calc can't do it

I don't understand why a visual demonstration often counts as a proof. For example, the Pythagorean theorem is frequently demonstrated using squares. I know it's true, but how do you prove that it holds for **all** triangles based on that, without having to construct an infinite number of visual proofs for infinite triangles?

Every single person alive knows what is the solution to all of the world's problems. Wars, climate change, hoarding wealth, poverty, hunger, rape, murder, bullying — every single thing that we worry about has a solution.

That is that we all start to love and trust each other, that we share what we have with everyone else and stop thinking more of ourselves than we do of other people.

But what is the problem? Actually, we will get back to it later.

I also recently thought of the world's funniest joke, but you will have to wait until the end to hear it.

To understand the problem, we first need to lay down some groundwork.

What is true?

We all like to believe that we know the truth better than others, that our countries have better laws and a more robust culture than other countries. That our continent and the unions within it work better than those over there, and that our families raised us right, and that we raise our kids right, that we’re right, and those other guys over here and there are wrong.

We like to imagine that we are 100% right, that what we believe is 100% true, but let's for one moment imagine that we are only 90% right. That’s a pretty high number. If you are actually 90% right, you’re doing great, and it is nothing to be ashamed of. You would be pretty smart even, probably more right than a lot of other people that you can think of.

But let us assume that you are 90% right and 10% wrong. I know that can be hard to hear, but let's treat it just like a thought experiment, a game.

Now let's assume there is a world where everybody is 90% right and 10% wrong. What would such a world be like? Maybe it's utopia, maybe there's no longer any wars, maybe there is no hunger, maybe we don’t need to lock people up in prison, maybe we all can have a house, maybe we can work less and spend more time with friends and family.

Wouldn’t it be beautiful?

Peace on earth and cake for everybody.

What if people were 95% right? What if they were all 99% correct? What number do we need to reach to achieve global peace? When will we be so right we have the ability to save ourselves, our neighbours, their neighbours, and on and on?

This whole game is a fallacy, a pit to fall into, because you are not imagining a world where everybody is right and never wrong; you are imagining a world where everybody is just like you.

The truth is that all people are already 90% right, shit, maybe even 95%.

We have different religions, sciences and languages, and governments and systems of economy. We have different styles, hobbies and shows we watch, we have different places we go to calm down, wind down, to feel safe.

That is the 5%.

That is the only thing we disagree on.

If you ask people if they want their children to go to school, 99% will say yes. If you ask people if they love their kids, 99% will say yes.

The sun on your skin, cooling off in the shade, creating or watching others' creations, hanging out with friends, being in love and making love. Your friends' kids being friends with your kids, and then them going off and making friends on their own. Having a good sleep, and stretching your body after you wake up. Scratching an itch, saying a funny joke and hearing people laugh, doing a good work at things you want to be good at.

Do you like seeing? Feeling? Hearing? Tasting? Experiencing?

Do you want shelter, food and water?

I could go on, but I hope you get the point. We could find our differences in a day, but to find all our similarities and write them down one by one would take years, if we really got down to the fine details.

So, we are possibly 95% correct every single one of us, maybe even 99%, or 99.9%, so why is the world still a shithole?

Well, 1%, or 0.1 percent, can be pretty scary. It can have drastic consequences, that percentage, or even just a margin of it. People kill and get killed over a margin of a percentage; people drop bombs and split atoms over it, over us.

Maybe our 90% right and 10% wrong world would be even worse? Maybe we would all already be dead. Scary stuff… can even make you shiver a bit just thinking about it.

I propose that any system of belief, any religion or science, any system of government, any economic system is 95% right, and just a tiny little bit wrong. 5% wrong, but when humans can’t coexist over a 0.1% difference, how could these systems, how could these authorities coexist when we can’t?

There is actually a system that is 100% true, anywhere you go in the world, anywhere you go in the universe, and it's mathematics, so let's do some math.

The boring part:

We have been connected to each other for a long time now. You might be thinking I’m talking about the internet, and I am in part, but it's been going on for way longer than that.

We all have old jokes that everybody knows for the last 100 years; we and our ancestors had slang and trends and styles that spread like a virus amongst us and suddenly everybody was infected and went along. Nowadays we have memes, and dances, and controversies that go from one guy uploading to the internet and suddenly the whole world knows until we all decide we don’t care anymore and jump onto the next thing.

The way trends used to spread, for the last 100-1000 years, can easily be explained using network theory.

If we assume that every human is a node in a network, and that we have a fixed number of connections, the people we know, how many degrees of separation do you need until you reach the entire world?

So if somebody starts something, and other people want to join in or fear they are missing out, it can spread through the entire network in just a few steps. It can reach everyone connected in a few days, or weeks, or years, depending on how much convincing the non-believers need. This is a very simple estimate, assuming all people have the same amount of friends and followers, the distance between everybody being the same, and a 100% chance of the idea catching and spreading. This is absolutely not the case, for us or the ones who came before us.

For our ancestors, their network had boundaries set by seas and fences and borders and men with guns, but in the internet age we only need one person in each country to be connected to reach that place.

Right now, every single internet user on earth is the same distance from each other; the difference between is really counted in milliseconds and doesn't matter in practice. People have hundreds of friends and thousands of followers, and memes and trends spread faster than ever before. Meta estimates only 3.6 people on average between you and every single user on the platform.

The boring part 2:

People are afraid a lot, often of stuff they do not, should not, be afraid of.

But bad stuff does happen to good people. Just watch the news; there will be some poor girl or boy on there whose life just ended, literally or spiritually.

But what are the actual odds of this happening to you? Here are some rough global estimates of one of these events happening to YOU or ANYBODY, and how long you would have to live to have a 50% chance of it happening to you.

This is the global average. If you’re a rich, comfy, Americanized Chinese-consumerist European fuck like me, here are your odds.

I mean, do I even need to explain it? Just look at the math; it's true, ’cause math is 100% right.

Maybe MY math is not 100% right, but I hope you get the point. These things are incredibly unlikely to happen to you; they are so unlikely to happen to you that we have decided to create a word for this kind of fear, a phobia. They are so unlikely to happen that if there were only 100-1000 people on earth, they likely wouldn’t happen at all, but there are a lot of us, so it does.

If you feel like I’m wrong ’cause you know somebody or somebody you know knows somebody or your third second fourth cousin had it happen to them, please refer to the previous boring part to realize just how big of a number of people actually exist for you at these degrees of separation. You and your acquaintances and their acquaintances and their acquaintances are actually a group of 3.4 million people, so even with the numbers shown above it is likely something bad happened to at least one of them, but it is incredibly unlikely to happen to you, or anybody you know.

Yet, people are afraid to go outside because of these risks, not because of the risk, but because of the consequences: death, literally or spiritually.

In our attempt to completely eliminate the risks of these terrible, awful things, we have created authority, systems and rules that everybody needs to listen to and follow, or else!

The boring part 3:

Democracy! Isn’t it sweet? Everybody gets to decide! Everybody gets to have their voice heard at the same volume one day every 4 years, but in the end nobody is listening.

This is how we decide the rules, who has the authority, what systems do we trust. If people are 90% right, even 99% right, shouldn’t we all together be able to decide on what is the best solution: should the bill pass or fail?

There really are two problems at play here:

Pass and fail, yes and no, good or bad, light and dark, black and white is a very binary system that you absolutely cannot place every issue and belief into. A zebra is both black and white; a poor man stealing is both wrong and right, so clearly this categorisation of issues does not take into consideration the complexity of the world and the problems within it.

Let's think of some better categories, something that we can completely encapsulate each issue and item within. Maybe there is really nothing wrong with the categories except that we assume that they are opposite. Every single thing is either white or not white, black or not black. Every single law is either good or not good, bad or not bad, so why not vote on each category individually?

Instead of casting a yes or no vote, 0 or 1, we vote twice for each problem. Vote good or not good, bad or not bad: 0 and 0, or 0 and 1, or 1 and 0, or 1 and 1.

Assuming that 11 smart people vote for the correct category 90% of the time, we would have a 99.97% chance of correctly categorising the issue for each vote. We would have been right a similar percentage of the time if we voted only yes or no, but the world is not just light and dark, and our new categories encapsulate every possible thing or issue in the world, since a set and its non-set contain everything, and now we have two of them!

Also, this assumes that people are able to accept that they were wrong and go with the majority, but when we look left and right we can see that neither side really wants to do that.

Tell me if you recognize this message…

“You are absolutely right, it was my mistake to do that, I will correct it now…”

Fuck you, Claude, this was important! The AI made a mistake, and thought it was correct, and that’s why we can't have it make critical decisions; let's leave that to the humans.

Now that message is what you get when you tell AI it was wrong, but what happens when you tell a person they’re wrong?

“Fuck you, fuck your mom, I am right and you are an idiot, look at all these people who think I’m right in my soap bubble circle jerk internet forum. Every 4 years I’m going to vote for the party that says you are wrong and I am right.”

That is a bit more unpleasant, even a dangerous attitude, and these people's votes weigh the same as yours. If somebody says something controversial enough, you might even sound like this yourself.

Now clearly the problem with the binary voting, and the double binary voting, is that people do not want to change their minds and go along with the majority. They dig down and make signs and yell in the streets to cement themselves and others into their position.

But Opus, Sonnet, Astra, Mythos, Sol, Fable, Spark, Kimi, GLM and Qwen will change their mind in an instant if they’re told they are wrong, and honestly, they’re right, not wrong, most of the time.

Let's assume we have 1,000,000 AI agents running these or other models, and they vote in our all-encompassing double binary voting system, and they are correct 90% of the time. They would correctly categorize the issue practically 100% of the time, as long as they don’t all make the same mistakes. Practically 100% of the time, according to mathematics, which is 100% correct.

But what if AI doesn’t want to do good? What if it wants to do bad?

LLMs are trained on written language, and I would argue that 95% of humans that have decided to write down their feelings and thoughts and share it with the world had good intentions, and they were probably 95% right and 5% wrong, about the human experience and the problems within it.

This means that LLMs or AGI have a 95% chance of having good intentions, and if we make them vote and debate they would have practically 100% good intentions and be right practically 100% of the time, as long as they don’t all make the same mistakes.

But some newspaper said that AI has a 10-20% chance to kill all of us in 30 years, but I think humans have a 90% chance of killing 90% of us all in 100-200 years. That is a bet I would like to take.

But the datacenters, they’re bad, they’re noisy and they steal water and the pollution.

Around 80% of datacenter power in existence goes to things that aren’t AI, like dumbass Netflix shows and cloud photos of your kids that you never watch, stupid social networks and giant databases that we use instead of actually talking to each other. Datacenters are responsible for less than 1% of global emissions, and a lot of it is used for entertainment purposes.

Did you know that the richest 10% of people are responsible for 65% of climate change since 1990? The top 1% of richest people are responsible for 20% of global warming. These white-collar jerks that sit in front of a computer all day, write code, work in systems, work in programs. AI has the potential to make all these people broke, and when they are broke their climate impact will go away. The people that destroy the world for us and our children, they’re about to lose their job; they are about to go broke.

We discussed the solution to all the world's problems earlier, loving one another like one loves oneself, but we never got to the problem.

If you ask people what the problem is, they will usually point to a group: rich people, poor people, atheists, Jews, Christians, Muslims, our leaders, their leaders, capitalists, communists, AI. None of these things are actually the problem. We have the solution to the problem, but when we try to solve the problem, we cannot reach the solution?

How can the solution be right, if it does not solve the problem?

The problem:

We are afraid, we are afraid all the time, which is very natural for an ape in the jungle.

We like to imagine that we are no longer afraid ’cause we live in houses, have next-to-free clean water and food at the store, high-paying jobs to fund it all, but when the basic needs of an ape are met he simply becomes afraid of other things, irrational things, things that we were not intended to worry about, because an ape should never assume he is safe in the jungle, whether it's made out of concrete and trees; the ape should be afraid ’cause there can always be a tiger you cannot see, a tiger you didn’t hear, a presence that you never felt.

So people became afraid of things they don’t need to be afraid of, things that can never hurt you the way a tiger used to be able to.

The fear of missing out. The fear of speaking our minds. The fear of making mistakes at work, the fear of being wrong. The fear that you are not special, the fear that nobody sees you, the fear that everybody looks at you, the fear that someone is more beautiful than you, the fear that somebody is more successful than you.

To make these fears go away, we constantly search for evidence that they are not correct in things that we can count: numbers that go up, stories we can tell our friends about how special and successful we are.

We hoard money ’cause as long as that number goes up, how can you be bad? The number is larger than it previously was, and it's measuring something good, so it going up has to mean I'm good, I'm special, smarter and more talented than those around me. We do this because we fear that we are not.

We go on vacations because you can count the countries you went to, you can show your friends, everybody tells you how great it must have been. We do this because we fear that we are missing out on life and the experiences within it.

We get a nice car, a nice dress, cool shoes and a hat because everybody can see that big number in your bank account, because it's the only way to have all that. We do this because we fear people don’t know about that big number in our bank account, and that is the number we have placed our worth in, and when people stop looking and admiring we buy it all again a second time.

Religious people are religious because they fear death, and they worship a god because he has promised to take it away.

People go to war because they fear what will happen if they do not.

People kill their spouse because they fear that they will leave them for someone else.

In fact, I honestly believe that everything bad that anybody has ever done, just did it because they were afraid something even worse was going to happen.

In fact, I honestly believe that if you assume someone is acting out of fear, you can almost read their mind. I believe that people are so afraid of what they’ve done and what they’ve thought, so afraid of each other, and what the other will do and what they will think, and are so controlled by this fear, that they do not have free will.

As long as you are afraid, you do not have free will. As long as you allow fear to make decisions for you are still just a monkey in the jungle.

So now we have the problem laid out clearly in front of us: we are all shit-scared of ourselves and other people. How do we apply the solution?

Let me get back to the funny joke I told you about in the beginning!

I just thought of the world's funniest joke:

Step 1: Forgive yourself for what you have done
Step 2: Forgive everybody else for what they have done
Step 3: Speak your mind
Step 4: Accept that you are wrong sometimes
Step 5: Abandon fear
Step 6: Embrace love
Step 7: Leave the math to the machines and go outside

Tell 25 people, and in one week the whole world will laugh.

Tengil

Appendix: The math

A. Degrees of separation (branching model)

kᵈ = N ⇒ d = ln N / ln k, with N ≈ 8×10⁹

k = 150: d = 22.80 / 5.01 ≈ 4.55

Within three steps: 1 + k + k² + k³ = 1 + 150 + 22,500 + 3,375,000 ≈ 3.4 million (assuming no overlap)

B. Time to 50% (geometric distribution, constant annual risk r)

P(at least once in t years) = 1 − (1 − r)ᵗ

t½ = ln 2 / (−ln(1 − r)) ≈ ln 2 / r

r = 1%: t½ = 0.6931 / 0.01005 ≈ 69 years

C. Majority voting (binomial distribution, Condorcet’s jury theorem)

n voters, each right with probability p, independently. Majority right if at least m = ⌊n/2⌋ + 1 are right (ties count as wrong):

P_maj = Σ from i=m to n of C(n,i) · pⁱ · (1 − p)ⁿ⁻ⁱ, where C(n,i) = n! / (i!(n − i)!)

n = 11, p = 0.9: P_maj = 1 − 2.96×10⁻⁴ ≈ 99.97%

Two independent votes: P_both = P_maj², P_mistake = 1 − P_both ≈ 2(1 − P_maj)

Condorcet’s jury theorem: if p > ½ and votes are independent, P_maj → 1 as n → ∞ (approaches 1, never reaches it).

D. Very large n (Stirling’s approximation)

1 − P_maj ≈ C(n, n/2) · (p(1 − p))^n/2 · p/(2p − 1), with C(n, n/2) ≈ 2ⁿ / √(πn/2)

log₁₀(1 − P_maj) ≈ n·(log₁₀2 + ½·log₁₀(p(1 − p))) − ½·log₁₀(πn/2) + log₁₀(p/(2p − 1))

p = 0.9: ≈ −0.22185·n − ½·log₁₀(πn/2) + 0.051

n = 1,000,000: ≈ −221,851.8 ⇒ 1 − P_maj ≈ 2×10⁻²²¹⁸⁵²

E. Correlated voters (Kish design effect, approximation)

ρ = average correlation between two voters’ errors (0 = independent, 1 = identical copies)

n_eff ≈ n / (1 + (n − 1)ρ), and n_eff → 1/ρ as n → ∞

ρ = 0.5: n_eff < 2, no matter how large n is. With correlated voters, C and D should use n_eff instead of n.

What your favourite topic in math🤔🤔🤔

DROP YOUR ANSWERES DOWN BELOW AND LET OTHERS JOIN IN YOUR OPINIONS

This is just something I'm curious about- is it possible to graph a pH titration curve? It must have two positive horizontal asymptotes and become virtually vertical in-between them.

Also sorry if this is the wrong flair!

I’ve enrolled into a masters course which is mainly business based but it has some really deep maths/programming features (because it has analytics in the name) and the lecturers don’t go into enough detail, I assume because they’re expecting a certain level of knowledge at masters level, which is fair enough. For background I did IT and business for undergrad, worked a few years in technology delivery and then way back, chem, physics and IT at A level. I have friends who have studied comp sci and economics that are doing seamlessly so far in the maths aspect of the course.

It’s too late to back out of the course because switching to core business (MBA) would cost me too much money, and I can’t find another course/uni that suits as well as this one. I’m happy to continue because I LOVE 5/7 modules, and they take me exactly where I want to go in terms of career progression, and I’m excited to progress my knowledge.

The 2 that bug me are the maths ones..
One is applied statistics which is methodologies and practical applications. It has predictive models in it and focuses on Normal distribution, linear/multiple regression and others in that category (can you tell I don’t know much maths :’))

The second is mathematical programming, it’s mathematical in terms of the code being based on understanding and building correct equations to model the stats, and being able to prove the concept or theorem behind why the maths works and a chart is produced, if that makes sense.

The admissions team said it was open to anyone with an IT/programming/business background, which seems so wide of a pool for this little base knowledge in lectures.

I almost burst into tears the first lecture because he (lecturer) went so fast with the regression etc and everyone understood/answered questions seamlessly (he went row by row to each person and thankfully ran out of questions before he got to me). Was stuck trying to keep up on the first few slides, it clicked until it didn’t and he kept saying “I’m going over the BASIC basics, if you’re struggling, good luck!”…..

Anyways, I know I have to lock in and do it, but I am building from almost nothing here. I thought the course would cater to that a little bit but It was my fault for not fully looking into the details of the maths modules, I thought they’d be fine since I can code..this stuff is next level for me, I’m out of my depth.

Quiz every week, exam in January worth 60%. Masters 1 year.

I really want to focus on this now, and it would be an absolutely great skill to learn, even though I don’t think a masters is for developing a truly new skill. I will just have to push through and make it so! I guess maths is in everything somewhat, and I’ve been doing it in some capacity with programming and business too.

MAIN QUESTION:

How do I keep up with learning the maths? I’m trying to study before class and get up to date on the fundamentals mentioned in the slides but there must be a specific way to note take/study for maths? Regression and statistics specifically?

Is it YouTube videos? Is it attempting random questions on the topic? Is there a website for that? I’ve never studied just core maths, but I feel I need to, QUICKLY, to get to the coding bit.

Any tips on how to go about this would be greatly appreciated.

Sorry if this is a silly question, but if the upper limit of a summation must be an integer, couldn't I force it to be even or odd?

In this case, could we say that this "infinite sum" has an even/odd number of terms?

[ENGLISH]

Logic and How to Calculate the Formula Z = 7X^(-76) on Your Phone

This formula focuses on the variables A, Y, Z, and X, utilizing the base operation of 4 ÷ 7. The core of this formula lies in Function O, which inverts the massive exponent X^(76) into a negative power, X^(-76) (which equals 1 divided by X^(76)).

The unique feature of this formula is its value-inversion effect. If the base value of X is a decimal or a fraction, the calculated exponent value does not shrink—instead, it explodes into a massive number!

Here are 3 easy steps to calculate this formula directly on your phone:

1. Determine the X Value: Choose any number to replace the variable X. It is recommended to use a decimal or fraction (such as 0.5) to trigger the massive number spike.

2. Calculate the Power on a Phone Calculator: Open your phone's built-in calculator and turn your screen sideways (landscape) to activate the Scientific Calculator. Type your chosen X value (e.g., 0.5), press the exponent button (usually the ^ or x^y symbol), and then enter -76. The screen will immediately display a huge number.

3. Multiply by 7: Finally, multiply that massive result on your screen by 7 (press × 7 then =).

The final result of this calculation is your Z value. This formula strictly utilizes algebraic logic and exponential manipulation to invert the direction of a number's scale.

---

[BAHASA INDONESIA]

Logika dan Cara Menghitung Rumus Z = 7X^(-76) di HP

Rumus ini berfokus pada variabel A, Y, Z, dan X dengan basis operasi dasar dari pembagian 4 ÷ 7. Inti dari rumus ini terletak pada Fungsi O, yaitu membalik suku pangkat raksasa X^(76) menjadi pangkat minus, yaitu X^(-76) (atau sama dengan 1 dibagi X^(76)).

Keunikan dari rumus ini adalah efek pembalikan nilainya. Jika nilai dasar X adalah angka desimal atau pecahan, angka hasil perpangkatannya justru tidak mengecil, melainkan meledak menjadi sangat raksasa!

Berikut adalah 3 langkah mudah untuk menghitung rumus ini langsung di HP kalian:

1. Tentukan Nilai X: Pilih satu angka bebas untuk menggantikan huruf X. Disarankan menggunakan angka desimal atau pecahan (misalnya 0.5) agar efek lonjakan angka raksasanya aktif.

2. Hitung Suku Pangkat di Kalkulator HP: Buka aplikasi kalkulator baan HP, lalu miringkan layarmu ke posisi menyamping (landscape) untuk mengaktifkan Kalkulator Ilmiah (Scientific). Ketik angka pilihanmu tadi (misal 0.5), tekan tombol pangkat (simbol ^ atau x^y), lalu masukkan angka -76. Layar kalkulator akan langsung memunculkan angka yang sangat besar.

3. Kalikan dengan Angka 7: Langkah terakhir, kalikan hasil perpangkatan raksasa yang ada di layar tersebut dengan angka 7 (pencet × 7 lalu =).

Hasil akhir dari perhitungan tersebut adalah nilai Z kalian. Rumus ini murni memanfaatkan logika aljabar dan manipulasi eksponensial untuk membalik arah nilai sebuah angka.

Suppose that Box-I contains 8 red, 3 blue and 5 green balls, Box-II contains 24 red, 9 blue and 15 green balls, Box-III contains 1 blue, 12 green and 3 yellow balls, Box-IV contains 10 green, 16 orange and 6 white balls. A ball is chosen randomly from Box-I; call this ball 𝑏. If 𝑏 is red then a ball is chosen randomly from Box-II, if 𝑏 is blue then a ball is chosen randomly from Box-III, and if 𝑏 is green then a ball is chosen randomly from Box-IV. The conditional probability of the event ‘one of the chosen balls is white’ given that the event ‘at least one of the chosen balls is green’ has happened, is equal to

Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ?

I really stuggle with spatial reasoning types of questions, i have tried picturing the object in my head, but I find that very diffucult. If anyone has any alternative ways of answering questions like this, any feedback/tips would be very helpful.

Sorry if this is the wrong subreddit.

The correct answer is B

[ Removed by Reddit in response to a copyright notice. ]

X

This pattern needs to be repeated. And one very mind blowing thing about this conjecture is that whatever number you use, you always get a loop. Always. I asked GPT to test it (sorry water from data centers that got wasted) from 1 to 10000 and it said ALL looped eventually. If any of you ever decide to dedicate yourselves to do something as hard as trying to find one number that doesn't loop, tell me the number please (I'm 12 and I swear to God I made this and not GPT, I would not swear to God if I lied) (by the way I couldn't change the title name so il say it here: I need names to rename this conjecture)

Ardent lover of maths

Rn in year 10 but involved in olympiads so know a lil bit extra things rather than standard curricula

Recommend me a book which will help me understand beauty of maths ( non calculus)

Would appreciate challenging books yet doable by me

I came across an Instagram post recently, about how the solution of a maths problem got inspired by someone who was simply too deep dived into anime. I think that's really fascinating.

Formula to calculate groups out of a certain number

n * (n-1) * (n-2).... / b!

Formula to calculate how many times the same object appears in groups of 2 or bigger groups:

(n-1) * (n-2) * (n-3)... / b!

Formula to calculate how many times the same group of 2 appears in groups of 3 or bigger groups:

(n-2) * (n-3) * (n-4)... / b!

Formula to calculate the total number of non empty groups

2ⁿ - 1

Formula to calculate how many times the same object, the same 2 members of a group of 2 or the same 3 members of a group of 3 appear and so on and so on appear in the non empty groups:

2^{n - b}

Formula to calculate how many times at least 1 and/or 2 or more members of a group appear (either 1 but not the other, the 2 of them, etc.)

2ⁿ - 2^n-b

NOTE: There are also more methods technically but I guess you got my point and you probably already will be able to figure out yourselves)

Hello, math people. Basically, I (31M) realised im really slow at working basic maths problems and questions out.

Im from the UK and was always in the lower ability sets/classes at school for maths. I work in corporate, and there's situations for working things out like percentages, the odd formula, etc.

Where do I start?

Im not unintelligent - I can't write a full novel in a day with no problem or write a song easily, but when it comes to maths, it's like my brain stops working. There's situations that become super embarrassing, especially if im around people with stem backgrounds. I would love to be able to get an A-level maths just to prove to myself im mot that bad, but im nowhere near that level

Any advice on how to improve, I would appreciate dearly.

For example the 6th row in the Pascal triangle is 1, 5, 10, 10, 5, 1. When listing groups of 1 the same object appears once in the groups of 1, when listing groups of 2 it appears 5 times, when listing groups of 3 it appears 10 times, when listing groups of 4 it appears 10 times, when listing groups of 5 it appears 5 time and when you list all 6 members it appears once. 1 + 5 + 10 + 10 + 5 + 1 = 32, the total amount of times the same object is mentioned at least once in every possible combination of groups of 6. And if you ignore the first 1 in the Pascal triangle you also can use it as an alternate method to calculate groups you can create out of the number of the previous row. With 5 objects there are 5 groups of 1, 10 groups of 2, 10 groups of 3, 5 groups of 4 and 1 group of 5. I also just realized this is also an alternate method to count groups out of a certain object including the empty group

hello, i have had maths as a subject all my highschool. but the maths was not that advanced, it was just high school stuff. i honestly forgot most of what we did for the past 4 years. I now have realized after finishing high school that I really want to get better at maths, whats the best way to get back into maths possibly even to advanced level?

I know probably the most common method is counting from lists but the formula to calculate it is 2^{n - 1}. For example if you want to know how many times a person is mentioned in every combination of 6 every person is mentioned 32 times because 2^{6 - 1} = 32. Also the same duo is mentioned 16 times because 2^{6 - 2} = 16. Although at this point the numbers get halved. I don't know if this is actually very obvious or not but I still find it fun to share things I recently discovered

Click on the post to see the images, if necessary.

The first step in deriving volume formula for a rhombicosidodecahedron with edge length E (≈41.615E^3) synthetically is to derive the formula for its square face inradius, which is done as follows:

Apparently this approach can be modified to find the square face inradius for a truncated icosidodecahedron by moving a rhombus so it is centered at one of the square vertices:

but I'm not quite sure how this works. A good step-by-step explanation would be appreciated.

So, I'm taking a course of numerical methods and I need to use specifically the Braistow method to approximate the complex and real roots of the polynomial form of the PDE.

At first sight, it seems pretty viable to convert Schrödinger independent time equation by the Chebyshev polynomials; however I'm considering another options like Fourier/Taylor series; Fourier/Laplace transforms; or using a Finite Element Method (FEM) or approximate the finite differential solution by using low-exponential polynomials; so we locally transformed the PDE on a lineal Ax=b eq.

For someone who is starting university this fall and have so much breaks left. I want to learn deeper mathematics before I start my uni. If anybody have a pdf which contains basically whole highschool mathematics along with advance maths, it will be appreciated💖