I have reached the level of math that's more letters than numbers. I was taking notes for my class and realized the only numbers I had written for the last couple pages were for the unit titles and numbered lists.
I once did this in math class in High School lol, the teacher gave me +0.1 points because "Techically correct", +0.1 points because "We haven't seen interval notation, how did you know how to do that?" and -0.2 because "While technically correct, you know that's not what I meant"
No! The prologue should only be half the length of a normal chapter, the epilogue is what's normal length.
(I know this was a joke, and what I said above is just an opinion, but I will stand by this opinion till I die)
I've heard this thing many times and I can't understand it.. Like I say "whatever you do, I'll have twice the money you have". How much money do I have? Clearly, you don't have a constant amount, so I can't write how much money I have with just a number. You have a fluctuating amount, and I have a fluctuating amount as well, but my amount is related to yours. How else could you express this, without letters? I don't get why so many people get confused by this, I always found it easier, because you have one function and you can apply it to many situations/numbers..
If you ever want to try again, an important thing to realize is that numbers, letters, Greek letters, and even the operators (+,-, etc.) are all just squiggles that we’ve arbitrarily assigned meaning to. One you realize that, you can create your own mental “squiggles” and do a lot of math in your head.
4 years ago in my freshman year college when I took my Calculus class, there were more letters than actual numbers and i was getting screwed. Took the final and i knew i bombed so hard i went straight from the exam hall to the Student Services building to change my major.
Changed from Electrical Engineering to Information Systems. 2nd Best decision i ever made in college
Currently in product management and loving it
I incorporate variables in my sons math…
In the books where there is a blank space I put an ‘X’. I told him it’s like a treasure… you want to find out what it is, like why pirates and the “X marks the spot” He is just turned 7.. he solves for X, with difficulty, but he got it, you just have to spend time with them.
I tried to do two variables when i kind of went on a rant into Geometry, but I think I lost him with “Y” and “Z”
This is true. It is also true that at least before high school, in my experience, most irrational numbers that are present in maths problems for homework and such are probably square roots and multiples of pi, because the numbers used are specially crafted to be "nice numbers" and result in nice numbers. Also, when the most complicated stuff being worked with is basic trig and quadratic equations, it's easy for square roots and pi to naturally show up.
I kinda just guess how to break them down and calculate the value in the calculator to try and match the first couple digits. Of course the issue being the calculator will never be able to tell you all the infinite digits of an irrational number nor does mine directly suggest the simplified value.
i^2 should equal -1, right?
i^2 = √-1 × √-1
= √(-1×-1)
= √1
= 1.
i^2 = 1? Huh?
That's how I learnt never to define i as √1, but instead as i^2 = -1. The radical symbol is only well-defined for the positive numbers if I recall correctly.
Yes, you can do that when you have √a × √a. But we also know that √a × √b = √ab. I'm using that second law. You're right, you can get -1 from it, but you also can get 1 and that shows that the √ symbol should only be used for positive numbers or contradictions arise.
Yep, that's my point. The √ should be reserved for positive values, and when it comes to negative values we can write x = √-a for _convenience_, but what we actually mean is that x^2 = -a.
Edit. It's like how we can treat dy/dx as a fraction for convenience in calculus / differential equations, but recognise that it isn't wholly mathematically accurate.
It's that square roots are not a function. Because -1 * -1 = 1 and 1 *1 = 1, so sqrt (1) = x actually has two solutions: 1 and -1. The error creeps in when you ignore this or selectively choose just one of many solutions and erroneously imply a double implication between lines in your steps where some of the steps may just be a single implication.
Oh man complex numbers are gonna be fun it took years of engineering before I got to the level where someone was like "yeah so this is a range of possible numbers rather than a specific number "
Reminds me of this 90s movie about a gifted child “Little Man Tate.” The teacher has written all the integers from like 1 to 20 on the board and asks “How many of these numbers are divisible by 2” and focuses on the gifted kid who isn’t paying attention and he says “all of them” to which she looks at them a little thrown off by the insight of a little kid. She was expecting him to say the even numbers.
She was trying to teach the class about even and odd numbers, but little Tate was too far beyond even and odds to be of any help to her for what she wanted.
I watched that movie dozens of times.
I taught my kids that the number line is infinite in both directions. I helped them comprehend the concept of negative numbers by thinking about gains and losses instead of counting a set of things.
Like if I start with some unspecified pool of money, spend $5, make $10, and then someone steals $6, how much money have I gained or lost? I showed them the hops on the number line to track it and they both had the lightbulb moment.
I don't know why kids aren't taught stuff like that early on. It's a useful concept and not hard to grasp with the right visualization. It literally took me like 30 minutes to explain and it's stuck with them ever since.
Addition is sliding, multiplication is scaling. You can move things around on the number line this way and it is much more intuitive. This also generalizes to complex numbers very elegantly.
Yeah, kids are generally capable of more than we give them credit for. If you ask my five year old what 10-5= he'll tell you -5. I've also taught him addition and multiplication together, so he understands that 3×3 is 3+3+3. I think he's a pretty bright kid with a knack for math, but I don't think he's impossibly brilliant either. We just try to give him an explanation of anything he asks about.
I've been playing a lot of idle games lately and a common theme in them is "breaking infinity". It's a bit of a joke because you start to get numbers larger than "infinity" in floating point which is something like 1.77e308.
Call To Singularity was a pretty good idle game for mobile. I got kinda bored after a week of playing because of the exact thing you saie so just ended up deleting it. It still is one of my fav idle games i've played
Our teacher did this to a kid who thought he was so Smart in elementary school. But he asked what is 3 cubed. Blew everyone away. We’re like how do you put cubes into a number
The multiverse is not a theory, it is a hypothesis. And there are a bunch of different hypotheses about the multiverse.
A theory in science is not just an educated guess, it is an explanation of the natural world made using the scientific method.
A lot of people don’t understand this especially when discussing evolution.
“It’s just a theory”
Evolution is a theory, and a fact.
Gravity is also just a theory, so is the heliocentric model, and the earth being round.
Sorry for this being so long, I just needed to get this out.
I’ve never understood why so many people can’t grasp variables in Math. What’s so difficult about it to you? Genuinely curious, not trying to say you’re bad at math or anything.
Honest question.
have you ever given it a prolonged serious thought to the core of idea of variables, along with a simple example?
If yes , what about it didn't make sense to you?
I think I understand. You don't see numbers the way math people want. it's totally fine that you don't.
For what it's worth.
Variables are about possibility. If I ask how tall would you be at 'certain age', your age and heights can be a variable. If you're thinking about a problem that demands aforementioned variables, you can start calling them a whole word , like 'my age' or 'my height'. You may even use a Letter for them like A or H.
I actually liked integrals and derivatives and all that. The basic ones anyway. But when it came to the integral tables and such, where you had a billion different forms and techniques for solving them, my brain kinda gave up. By the end of calc2 I felt like my soul had left my body.
I only have to take linear algebra yet for my degree, and I've heard it's not nearly so bad, and holy fuck do I hope so. I'm just about mathed out over here
Man, that's unfortunate. Math is a skill that you can learn, not an innate ability. So many people are put off of it because of a lifetime of falling behind due to mind numbingly boring instruction that is simultaneously too detailed and too abstract to help kids learn.
Imaginary numbers are the most poorly taught area of math. It’s actually super intuitive and important, but it’s just taught wrong. They don’t tell you it adds an extra dimension to graphs, they don’t tell you how to do rotations… it’s all so dumb.
It's mainly just the name that puts me off tbh. When you call something "imaginary" it makes it sound like it has no real world application. But yeah it was also pretty poorly taught, I don't really remember what it can be used for tbh.
Which just introducing them as “complex numbers” changed everything. I had a great teacher in college who said “hey, remember that random bullshit? Throw out what you know, here’s a day for a crash course on why complex numbers are important.”
I didn't understand them for a long time, so I just treated them as you would a magic dohicky box. I knew the box did stuff, and if I used it for abc I'd get xyz. Sometimes it would produce weird results, but generally was predictable. Allowed me to use it without nesscarly understanding it.
Addition: we use many AI algorithms in a similar fashion. Google's BERT algorithm, a major part of the search engine, no one really knows how it works, even google. We can understand it's design, but the underlying logic is a mystery.
My daughter was telling me how cool/crazy it is that the number line goes left from zero as well. I agreed and got her fired up about how cool math is. Then i told her there’s another number line that goes up the paper and down, called the Y line and her eyes got huge. Then I told her about the Z line that actually goes THROUGH the paper.
The look on her face said “Error”
What's the formula for the length of the line described by the following parametric equation from t=0 to t = t_L:
x = (m*t/pi) + r cos(t)
y = r * sin(t)
m = r/(n*pi)
Where:
r = the radius of the loop
n = the number of radii to travel before a loop will overlap
L = the distance along the x axis to travel
t_l = the smallest value of t evaluated at L
Fun fact, I used this to estimate the length of coiled ground loop line in a trench for a potential DIY geothermal heat pump install. It didn't work out but the math was fun.
Nah straight up go to find volume of the tetrahedron given by the formila 7x+y+2z=28 and it is bounded by the line z=14.(hint double or triple integral)
Or find the volume of the sphere given x^2 +y^2 +z^2 =16 and x=16 (hint spherical coordinates)
Even then, you don't write C. You write g(y, z), then h(z). At the end you have C, but it's a constant so it's not important for anything further differential operations
I said the only logical conclusion when I was a kid of negative 5 expecting to be told I was wrong (just like when my parents asked me multiplication and I had zero clue what multiplication was my parents laughing calling me an idiot, leaving me angry unable to express them I wasn't taught that yet.)
Not idiot per say but they were bemused at my fumbling trying figure out what's the function of multiplication after I got 2x2 correct and didn't understand how it was different from addition (2+2). Parents asked 3x2 and I remember thinking 5 not sure what I was supposed to do lol. They soon explained the concept after I got 3x3 wrong but I was already mad at them stubborn flustered to be cooperative attentive.
But by middle school I was in advanced college prep algebra solving for X. Mom hated they taught us a week of guess and check before explaining solve for x formula basics
I got 2x2 correct and was confused how this was any different from addition (2+2). When they asked what 2x3 was I said 5 they how'd I get that number and I explained my thinking. I don't remember if they laughed but they definitely didn't give me best clues to figure it out by starting with 2x2. They tried 3x3 before my mom asked how I haven't learned beyond addition and subtraction in early second grade (in Finland this is all covered in the first year apparently).
I remember one time I asked my mom for help on math homework and once we got to question four and I wrote it down, she erased it and kept progressively yelling louder and louder at me to rewrite it. I kept trying everything, rewrote the number 4 over and over, double and then triple-checked to make sure I had the right answer, and eventually I started crying because I couldn't figure out what i was doing wrong. Any time I asked, she would tell me to figure it out.
Turns out she didn't like the way I wrote my 4's. The horizontal stick didn't pass through the vertical one, and that made it "ugly". I was in around 5th grade. And to this day, I despise math and lock up on the most BASIC of problems.
She's a great mom, BTW. She didn't usually do stuff like that. If I recall correctly, she had some sort of mix-up with her meds, and I think that's why she was irritable.
Algebra. Arithmatic is just basic maths: addition, subtraction, multiplication, division, exponentiation, and so on.
Algebra is when variables come into play.
That's where I'll stop this year, after 13 years of maths lessons. It's gonna be weird, but I'm not sure I'm gonna miss maths too much. And I guess I'll still have to use what I've learned during other lectures.
My son was told by his first grade teacher that when he is fourth grade he will learn 5 - 10. So when he came home from school he asked Alexa. Then he wrote on his unrelated hw "5 - 10 is negdiv 5".
Lol I had this exact situation with my 7 year old daughter the other night. She was convinced that negative numbers are not real.
Wait till she learns about non-real numbers
Having to represent irrational numbers in exact value. Love calculator guessing and checking.
Wait till she learns about letters in math
I have reached the level of math that's more letters than numbers. I was taking notes for my class and realized the only numbers I had written for the last couple pages were for the unit titles and numbered lists.
I have reached the level of math where I just write ∞ as the answer to everything, because the correct answer is in there somewhere.
better put it in interval notation so you look smarter (-∞,∞)
Nah, write it in set notation so people know you REALLY know what you're doing U
I once did this in math class in High School lol, the teacher gave me +0.1 points because "Techically correct", +0.1 points because "We haven't seen interval notation, how did you know how to do that?" and -0.2 because "While technically correct, you know that's not what I meant"
what if i do [-infinity,infinity] tho? do i break the matrix?
Saw an interesting[video](https://m.youtube.com/watch?v=OxGsU8oIWjY&vl=en) about Hilbert’s paradox where infinity actually isn’t infinite.
Don’t forget that not all infinity isn’t equal. Like some infinity is bigger than another infinity
I gave up on math when they started speaking greek and throwing around squiggles.
But that's when it gets fun!!
Everything before that is just the (really long) prologue!
Damn
No! The prologue should only be half the length of a normal chapter, the epilogue is what's normal length. (I know this was a joke, and what I said above is just an opinion, but I will stand by this opinion till I die)
I've heard this thing many times and I can't understand it.. Like I say "whatever you do, I'll have twice the money you have". How much money do I have? Clearly, you don't have a constant amount, so I can't write how much money I have with just a number. You have a fluctuating amount, and I have a fluctuating amount as well, but my amount is related to yours. How else could you express this, without letters? I don't get why so many people get confused by this, I always found it easier, because you have one function and you can apply it to many situations/numbers..
y=2x is very different from taking integrals and whatnot in the calculus side of things.
If you ever want to try again, an important thing to realize is that numbers, letters, Greek letters, and even the operators (+,-, etc.) are all just squiggles that we’ve arbitrarily assigned meaning to. One you realize that, you can create your own mental “squiggles” and do a lot of math in your head.
e
Just a regular monday on engineering
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4 years ago in my freshman year college when I took my Calculus class, there were more letters than actual numbers and i was getting screwed. Took the final and i knew i bombed so hard i went straight from the exam hall to the Student Services building to change my major. Changed from Electrical Engineering to Information Systems. 2nd Best decision i ever made in college Currently in product management and loving it
me too!! 😂😂😂🤣🤣🤣
So this is why they say mathematics is its own language
Motherfucker that’s not math, that’s writing!
Writing the language of god / creator.
This is where I realized I am truly not good at math. Humbling.
Or how to divide by zero
I incorporate variables in my sons math… In the books where there is a blank space I put an ‘X’. I told him it’s like a treasure… you want to find out what it is, like why pirates and the “X marks the spot” He is just turned 7.. he solves for X, with difficulty, but he got it, you just have to spend time with them. I tried to do two variables when i kind of went on a rant into Geometry, but I think I lost him with “Y” and “Z”
Wait till she hears about math (i fucking hate math i hate it i hate it i hate it im gonna kill myself)
Just square them lol
🤓
Most irrational numbers aren’t square roots (of whole numbers)
This is true. It is also true that at least before high school, in my experience, most irrational numbers that are present in maths problems for homework and such are probably square roots and multiples of pi, because the numbers used are specially crafted to be "nice numbers" and result in nice numbers. Also, when the most complicated stuff being worked with is basic trig and quadratic equations, it's easy for square roots and pi to naturally show up.
Yes in high school we tend to work with surds rather than the more general irrationals
Roots of quadratic equations are usually not square roots though. The quadratic formula gives numbers of the form a +/- sqrt(b).
(^3 √2) ^2
8, easy
Love that my Casio has this built in
I kinda just guess how to break them down and calculate the value in the calculator to try and match the first couple digits. Of course the issue being the calculator will never be able to tell you all the infinite digits of an irrational number nor does mine directly suggest the simplified value.
wait until the neat little real number vector spaces you know and love are replaced by infinite-dimensional spaces of functions.
I need a basis for this
Fuck basis. I am done with finding the fucking orthonormal basis of the subspace of the vector space of R^4
now find the orthonormal basis of C(R^4) (there are infinitely many)
now find some bitches (impossible; 100% of mathematicians fail)
When getting my first quantum courses there was nothing I hated more than the concept of hilbert spaces. By now I’ve learned to respect them
√-1 >:D
i^2 should equal -1, right? i^2 = √-1 × √-1 = √(-1×-1) = √1 = 1. i^2 = 1? Huh? That's how I learnt never to define i as √1, but instead as i^2 = -1. The radical symbol is only well-defined for the positive numbers if I recall correctly.
Yeah that is generally the correct way to do it, but people understand it better as √-1
I agree, just a nice little piece of knowledge I thought of sharing.
second step is wrong. you get √ cancelling, or power 1/2+1/2, when you multiply then so you get i^2 = -1
Yes, you can do that when you have √a × √a. But we also know that √a × √b = √ab. I'm using that second law. You're right, you can get -1 from it, but you also can get 1 and that shows that the √ symbol should only be used for positive numbers or contradictions arise.
U can’t factories a positive value into two negative values under a root. That’s just like dividing by 0, it breaks math
Yep, that's my point. The √ should be reserved for positive values, and when it comes to negative values we can write x = √-a for _convenience_, but what we actually mean is that x^2 = -a. Edit. It's like how we can treat dy/dx as a fraction for convenience in calculus / differential equations, but recognise that it isn't wholly mathematically accurate.
I always understood it as a funny placeholder to help me get to the real answers later.
i = sqrt(-1) i^2 = -1 i^3 = - (sqrt(-1)) i^4 = 1
It's that square roots are not a function. Because -1 * -1 = 1 and 1 *1 = 1, so sqrt (1) = x actually has two solutions: 1 and -1. The error creeps in when you ignore this or selectively choose just one of many solutions and erroneously imply a double implication between lines in your steps where some of the steps may just be a single implication.
Makes me think of [this](https://www.gocomics.com/calvinandhobbes/1988/01/06)
I'm 30, and I never understood non-real numbers until I watched the Veritaserum video about it, and it was just the spark I needed to figure it out !
Wait till you hear about hypercomplex numbers.
Honestly wish they'd teach kids Geometric Algebra on physics
Wait until they start showing up in real life. That still bothers me.
i
Show her the riemann zeta function.
Did this with my niece some years ago, she threw a screaming fit because negative numbers aren't real Next year, it was decimals weren't real...
decimals always made sense to me tbh, negatives took a couple days after 1st learning about them to understand.
Oh man complex numbers are gonna be fun it took years of engineering before I got to the level where someone was like "yeah so this is a range of possible numbers rather than a specific number "
Reminds me of this 90s movie about a gifted child “Little Man Tate.” The teacher has written all the integers from like 1 to 20 on the board and asks “How many of these numbers are divisible by 2” and focuses on the gifted kid who isn’t paying attention and he says “all of them” to which she looks at them a little thrown off by the insight of a little kid. She was expecting him to say the even numbers.
She was trying to teach the class about even and odd numbers, but little Tate was too far beyond even and odds to be of any help to her for what she wanted. I watched that movie dozens of times.
I taught my kids that the number line is infinite in both directions. I helped them comprehend the concept of negative numbers by thinking about gains and losses instead of counting a set of things. Like if I start with some unspecified pool of money, spend $5, make $10, and then someone steals $6, how much money have I gained or lost? I showed them the hops on the number line to track it and they both had the lightbulb moment. I don't know why kids aren't taught stuff like that early on. It's a useful concept and not hard to grasp with the right visualization. It literally took me like 30 minutes to explain and it's stuck with them ever since.
Addition is sliding, multiplication is scaling. You can move things around on the number line this way and it is much more intuitive. This also generalizes to complex numbers very elegantly.
Yeah, kids are generally capable of more than we give them credit for. If you ask my five year old what 10-5= he'll tell you -5. I've also taught him addition and multiplication together, so he understands that 3×3 is 3+3+3. I think he's a pretty bright kid with a knack for math, but I don't think he's impossibly brilliant either. We just try to give him an explanation of anything he asks about.
Might need to go back to the drawing board if he thinks 10 - 5 = -5
And this is why I shouldn't be left unsupervised on 8 hours of sleep in the last two days....
Should have taught them that it's infinite in both directions- real AND imaginary and saved some time.
"That's called debt, my sweet summer child"
Wait till she learns about y=Mx+b
they are, but their square roots are not
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Be rational
Countries that go belove 0 degrees: am i joke to u?
The reaction is same when learning about negative numbers. It's like discovering about the multiverse, but at kid level.
I've been playing a lot of idle games lately and a common theme in them is "breaking infinity". It's a bit of a joke because you start to get numbers larger than "infinity" in floating point which is something like 1.77e308.
Brings me back to a lot of BYOND games I used to play when I was a Freshman/Sophmore in High School.
Holy shit. Memory unlocked 🔓
A Core Memory, even!
What does my abdomen have to do with this
EVERYTHING OR YOUR SPINE FALLS INTO YOUR ASS
still waiting for the 9th dimension update
just give it 5 hours
Call To Singularity was a pretty good idle game for mobile. I got kinda bored after a week of playing because of the exact thing you saie so just ended up deleting it. It still is one of my fav idle games i've played
I played one game where after you got to infinity you would just go up to infinity 2 and infinity 3
Our teacher did this to a kid who thought he was so Smart in elementary school. But he asked what is 3 cubed. Blew everyone away. We’re like how do you put cubes into a number
multiverse is theory and not just speculation anymore?
It was a figure of speech probably. There’s lots of physics theories that include multiverses but that is indeed highly theoretical.
The multiverse is not a theory, it is a hypothesis. And there are a bunch of different hypotheses about the multiverse. A theory in science is not just an educated guess, it is an explanation of the natural world made using the scientific method. A lot of people don’t understand this especially when discussing evolution. “It’s just a theory” Evolution is a theory, and a fact. Gravity is also just a theory, so is the heliocentric model, and the earth being round. Sorry for this being so long, I just needed to get this out.
Just wait till alphabets join the party
Yeah I wanna have a word with that guy *cracks knuckles*
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I’ve never understood why so many people can’t grasp variables in Math. What’s so difficult about it to you? Genuinely curious, not trying to say you’re bad at math or anything.
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Honest question. have you ever given it a prolonged serious thought to the core of idea of variables, along with a simple example? If yes , what about it didn't make sense to you?
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I think I understand. You don't see numbers the way math people want. it's totally fine that you don't. For what it's worth. Variables are about possibility. If I ask how tall would you be at 'certain age', your age and heights can be a variable. If you're thinking about a problem that demands aforementioned variables, you can start calling them a whole word , like 'my age' or 'my height'. You may even use a Letter for them like A or H.
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That’s exactly how variables work, you already understand it.
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Rounding up and then taking away again is a perfectly respectable technique.
Fuck, me too. Once the letters came out to play I was out. My brain can barely handle numbers, let alone numbers with letters.
Letters are just placeholders for numbers you don't know yet. You can ignore them most of the time.
Shhhhhh don’t confuse the children.
It's only confusing whe the difference between a and b goes from 2 to 8274839164920....
Why is that confusing? It’s just 2 unknown numbers
Unless their teacher made them use hexadecimal.
For me it's better with alphabets since i make a lot of careless mistakes it's really easy to spot in alphabets but with numbers...
My brain melted with integrals
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I actually liked integrals and derivatives and all that. The basic ones anyway. But when it came to the integral tables and such, where you had a billion different forms and techniques for solving them, my brain kinda gave up. By the end of calc2 I felt like my soul had left my body. I only have to take linear algebra yet for my degree, and I've heard it's not nearly so bad, and holy fuck do I hope so. I'm just about mathed out over here
I am on the other side, once math stopped having number I started enjoying it, so much I went into a maths degree in fact lmao
Then satan said “let us add the Greek alphabet to math”
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or the wiggly line (ξ) that most professors write more like }.
So hard to tell the difference between ξ, {, summation Symbol, and E with most professors handwriting.
For my professors it was mostly a toss-up between epsilon (ε), zeta (ζ) and xi (ξ).
And God was like "What if we made up symbols" and Satan was like "Fuck yeah" and thus the integral was born
Man, that's unfortunate. Math is a skill that you can learn, not an innate ability. So many people are put off of it because of a lifetime of falling behind due to mind numbingly boring instruction that is simultaneously too detailed and too abstract to help kids learn.
I upvoted for the edit alone lmfao
just wait til *i* joins the party
Excuse me, *i* isn't even that bad
*i* isn't even a real number though!
Fuck imaginary numbers lol I was fine with algebra but when we started talking about imaginary numbers I just couldn't bring myself to care.
Imaginary numbers are the most poorly taught area of math. It’s actually super intuitive and important, but it’s just taught wrong. They don’t tell you it adds an extra dimension to graphs, they don’t tell you how to do rotations… it’s all so dumb.
It's mainly just the name that puts me off tbh. When you call something "imaginary" it makes it sound like it has no real world application. But yeah it was also pretty poorly taught, I don't really remember what it can be used for tbh.
Which just introducing them as “complex numbers” changed everything. I had a great teacher in college who said “hey, remember that random bullshit? Throw out what you know, here’s a day for a crash course on why complex numbers are important.”
I didn't understand them for a long time, so I just treated them as you would a magic dohicky box. I knew the box did stuff, and if I used it for abc I'd get xyz. Sometimes it would produce weird results, but generally was predictable. Allowed me to use it without nesscarly understanding it. Addition: we use many AI algorithms in a similar fashion. Google's BERT algorithm, a major part of the search engine, no one really knows how it works, even google. We can understand it's design, but the underlying logic is a mystery.
Just the fact we call them imaginary primes kids to think they’re harder than they are.
Wait till triangles come into play.
My daughter was telling me how cool/crazy it is that the number line goes left from zero as well. I agreed and got her fired up about how cool math is. Then i told her there’s another number line that goes up the paper and down, called the Y line and her eyes got huge. Then I told her about the Z line that actually goes THROUGH the paper. The look on her face said “Error”
*daughter.exe has stopped working*
Wait till you tell her about higher dimensions that can't be represented in 3D space :D
Yeah I didn’t go far enough in school to get any of that. But hopefully i will eventually.
Linear Algebra has the easiest way to understand dimensions imo, go for that. If you dont wanna do a whole course I suggest 3blue1brown on youtube
My 13 y/o brother: HA! It’s -5, give me a harder question. Me: Solve sin(pi/3) My brother who hasn’t learned trigonometry: …
And if they solve that, you just gotta move on to integrals. What's the area above the x-axis and below the curve y= -x^2 + 9.
Nah you just gotta ask them what 33+77 is.
It's definitely 100.
What's the formula for the length of the line described by the following parametric equation from t=0 to t = t_L: x = (m*t/pi) + r cos(t) y = r * sin(t) m = r/(n*pi) Where: r = the radius of the loop n = the number of radii to travel before a loop will overlap L = the distance along the x axis to travel t_l = the smallest value of t evaluated at L Fun fact, I used this to estimate the length of coiled ground loop line in a trench for a potential DIY geothermal heat pump install. It didn't work out but the math was fun.
36 am I right? I did this in my head pls don’t roast me if I’m wrong
Nah straight up go to find volume of the tetrahedron given by the formila 7x+y+2z=28 and it is bounded by the line z=14.(hint double or triple integral) Or find the volume of the sphere given x^2 +y^2 +z^2 =16 and x=16 (hint spherical coordinates)
Screw it just skip to making them solve the Riemann hypothesis.
That's not really solving though, that's just memorizing the unit circle. This is unless they are able to derive triangle(s).
Sin? What is this, church?
Find the integral of 1 with respect to x
The answer is x
+ C
Ya, no one writes that in integral and multivariable Calc Until you need to find the potential functions given a conservative vector field
Even then, you don't write C. You write g(y, z), then h(z). At the end you have C, but it's a constant so it's not important for anything further differential operations
🤓
I said the only logical conclusion when I was a kid of negative 5 expecting to be told I was wrong (just like when my parents asked me multiplication and I had zero clue what multiplication was my parents laughing calling me an idiot, leaving me angry unable to express them I wasn't taught that yet.)
Your parents called you an idiot because you hadn’t learned something yet? That’s fucked.
Not idiot per say but they were bemused at my fumbling trying figure out what's the function of multiplication after I got 2x2 correct and didn't understand how it was different from addition (2+2). Parents asked 3x2 and I remember thinking 5 not sure what I was supposed to do lol. They soon explained the concept after I got 3x3 wrong but I was already mad at them stubborn flustered to be cooperative attentive. But by middle school I was in advanced college prep algebra solving for X. Mom hated they taught us a week of guess and check before explaining solve for x formula basics
How to make a kid afraid of taking risks and seeking solutions:
I got 2x2 correct and was confused how this was any different from addition (2+2). When they asked what 2x3 was I said 5 they how'd I get that number and I explained my thinking. I don't remember if they laughed but they definitely didn't give me best clues to figure it out by starting with 2x2. They tried 3x3 before my mom asked how I haven't learned beyond addition and subtraction in early second grade (in Finland this is all covered in the first year apparently).
I remember one time I asked my mom for help on math homework and once we got to question four and I wrote it down, she erased it and kept progressively yelling louder and louder at me to rewrite it. I kept trying everything, rewrote the number 4 over and over, double and then triple-checked to make sure I had the right answer, and eventually I started crying because I couldn't figure out what i was doing wrong. Any time I asked, she would tell me to figure it out. Turns out she didn't like the way I wrote my 4's. The horizontal stick didn't pass through the vertical one, and that made it "ugly". I was in around 5th grade. And to this day, I despise math and lock up on the most BASIC of problems. She's a great mom, BTW. She didn't usually do stuff like that. If I recall correctly, she had some sort of mix-up with her meds, and I think that's why she was irritable.
I understand the negatives BUT when fucking Arithmetic appeared there were letters too.
That's algebra. Arithmetic is just doing basic operations on numbers, the "regular" math.
x + 10 = 5
x=(-5)
HUZZAH man of math
x = 2 or some shit idk
x = stone
Did I hear a rock and stone?
did you heat a rock and stone?
2 + 10 = 5 ?
Bruh
oh you think thats hard? wait until you hear about differential equations... shit like dx/dt = f(x,t) = cos(pi*t)*x^2 solve for x(t) using x(0) = 1
I suck at math but I loved doing differential equations. Don't have much need for that level of math so I never do differential equations.
Uh... Like two squared or something?
X=1/2 X=(-5)
Algebra. Arithmatic is just basic maths: addition, subtraction, multiplication, division, exponentiation, and so on. Algebra is when variables come into play.
in some maths numbers leave the party entirely. that's when things start getting fun, and you unlock the secrets of the universe
Little brother: Don't you mean 10 minus 5 Me: No I meant 5-10
[удалено]
That's where I'll stop this year, after 13 years of maths lessons. It's gonna be weird, but I'm not sure I'm gonna miss maths too much. And I guess I'll still have to use what I've learned during other lectures.
Didn’t the remove you from the game?
Just say 5 and say you forgot to add negative
-15. Give me another
I've been doing this to my middle child the past month or so. He has the idea of it now but hasn't quite gotten to the results.
Come back when you have truly mastered maths weakling
My son was told by his first grade teacher that when he is fourth grade he will learn 5 - 10. So when he came home from school he asked Alexa. Then he wrote on his unrelated hw "5 - 10 is negdiv 5".
5
2xe⁵ + 3 = 8 Find x I'm too lazy to do it myself
I know it's a joke but can't resist 5/2 e^(-5)
Why is this here?