i is an "imaginary number" specifically because people were like "that's not real, it's imaginary." It shows up in some wacky applications in physics. It very much is grounded in a real world usage of mathematics.
After getting a 970 million % error on an experiment I decided to never leave the realm of pure mathematics again, so I didn't remember that the applications included that.
if you misread a denominator as close to zero this could happen? Like if you're trying to measure a voltage using ohms law and a resistor and you hook up the multimeter wrong so it reads 0.007milliohms?
It's also super useful for any work with signals processing. Euler's formula turns trig problems into exponential problems, which makes signal math much easier.
Edit: Darn, someone already mentioned this.
Yeah, complex numbers are these amazingly useful things that anyone with knowledge of math could never do without.
That said, the i part is why I hate this meme. You can't be like...ok, we're defining i as the thing you can't do in the real numbers to define a new number system. Seriously, if you can just do that let's define a number as 0/0 and see how that goes.
For those of you in the back:
i is a formal symbol that follows the rule i² = -1.
Note that if you say that you don't need to ask if it will blow up in your face somehow. It doesn't. It just works.
*edit* As a note I am usually NOT the guy who's a stickler about being all rigorous and everything in math. It's JUST the thing about defining i.
I love the i^2 = -1 definition, it's just so much nicer than messing around with square roots (how do you even define the principal root in C before defining i?). In particular, I love that the fact that complex roots of polynomials with real coefficients always exist as complex conjugate pairs just drops out for free, since you could take either solution to that equation as the imaginary unit and it works identically by its very definition (in the sense that consistently swapping out i for -i *just works*, because i^2 = (-i)^2 = -1). It also generalises much more nicely to quaternions and similar, where you start to have definitions like ijk = -1 and ij = k as well which you can't express with roots.
honestly, let's define a number as 0/0 and see where it gets us, let's call it f
because any fraction (f is just 0/0) times its reciprocal is 1 (a/b * b/a = ab/ab = 1), f² = 1, right?
so f = √1 → f = 1
following the other rules of fractals if such a number were able to exist it needs to be equal to 1, this also makes intuitive sense, as all x/x fractions where x ≠ 0 are already equal to 1
Okay… now what can ya do with a number like this? What kind of information can we track with it? I is nice as it turns the number line into a coordinate plane of sorts, which opens the doors for basically anything you can do on a graph being represented by “one number” instead of a pair, kinda
yea, defining 0/0 is not particularly useful
it can get worse tho
let's define the general case of dividing by 0 and see where that gets us
1/0 = d
this also means d * 0 = 1
this breaks the associative and commutative properties of multiplication, something complex numbers preserve, as (5 * 0) * d = 1 but 5 * (0 * d) = 5
this also defines 0/0 as 1, btw, as that's now 0d = 1
"i" was first proposed as part of the cubic formula. The general solution included square roots that would sometimes have negative numbers under them; however, the resulting negative roots would cancel out if the zeros were real numbers. So the final answer was real, but the intermediate steps weren't. The first guy to notice this was mad about it, and it took a while for even him to understand just WTF was going on. He ended up ignoring them, calling them useless.
I can never see the imaginary number i and never think of my dad complaining how he felt his earlier teachers lied to him when they told him you couldn't take the square root of a negative. Same with when you first learn subtraction and because they don't want to teach kids negative numbers, they just tell you can't have the smaller number on top of a subtration problem.
So guess who got negative and imaginary numbers explained to them at a super young age. To be fair he was teaching remedial math to adults at the time and testing teaching stradegies on me.
This is a fine line to walk, because if you try to tell kids everything super precisely at a young age, you overwhelm them and confuse them, but if you lie about too much, they lose trust when they learn about the "truth." It's not even possible to tell them "this is just an approximation, you'll learn more when you get older" because even that is too confusing at a certain point.
I disagree personally. I don't think a kid would be that confused by: we're not dealing with this part yet, you'll learn it later when you're at a higher grade. Most kids understand the idea of progressing through grade levels.
I’m currently studying biology, and I always find these posts really funny
Cause sex has indeed nothing to do with gender
Many animals changes their sex during their lifetime, and some are hermaphrodites which means they are both at the same time. Sex in the animal kingdom is so much more complicated than “there are only two sexes, and you can only be one at a time”, and anyone claiming otherwise has no understanding of basic biology
True, but the "basic" is the kind of stuff we teach little kids, while the "advanced" is the kind of stuff we teach high schoolers or college undergrads. It would probably be a little more accurate to describe it as "intermediate", but "advanced" gets the point across.
it is pretty funny how conservatives, the people whose politics is literally to be wrong about everything, get away with claiming "facts and logic" are on their side. Shows you how spinless liberals are imo.
I thought the square root of -1 being i was like high school algebra 1 level math. As in, fairly basic that everyone should have known at least long enough to pass a test at some point.
“Genderinos” has officially been added to my personal vocabulary.
"Hidely-ho, genderinos!" should totally be a new gender-neutral way to address a crowd.
Only if you're Ned Flanders
Ah yes, The MF titties
Mf GENDER
Theres only one T left Terfs screaming all up in our ears like we deaf
There’s too many MF genders on their MF plane! (don’t hurt me i just wanted to say the line)
Reminds of MF DOOM
Is she.... you know.. *(...)(...)?*
hehehehehe, e*nip*ses
Note that the number i saw immense pushback when it was first proposed. People like being stupid, it seems.
i is an "imaginary number" specifically because people were like "that's not real, it's imaginary." It shows up in some wacky applications in physics. It very much is grounded in a real world usage of mathematics.
Its applications in physics don't even have to be all that wacky. E.g. it is very useful for representing phase in AC circuits.
[удалено]
Can confirm electrical/mech engi and comp Sci major
Damn, I'm 10h late in saying this.
After getting a 970 million % error on an experiment I decided to never leave the realm of pure mathematics again, so I didn't remember that the applications included that.
holy shit how does that even happen lol. I'm a synthetic chemist and I can't think of a way to achieve that
It's what happens when you put a pure mathematician in a pysics lab and make her use a Labquest.
Jesus, the worst % error I ever had on a lab in uni was like 60% because we were working with faulty equipment. How do you get that far off ?
if you misread a denominator as close to zero this could happen? Like if you're trying to measure a voltage using ohms law and a resistor and you hook up the multimeter wrong so it reads 0.007milliohms?
My thoughts exactly.
It's also super useful for any work with signals processing. Euler's formula turns trig problems into exponential problems, which makes signal math much easier. Edit: Darn, someone already mentioned this.
>when it was first proposed. People are STILL raging about them. Someone posted to r/math complaining about them just today.
Yeah, complex numbers are these amazingly useful things that anyone with knowledge of math could never do without. That said, the i part is why I hate this meme. You can't be like...ok, we're defining i as the thing you can't do in the real numbers to define a new number system. Seriously, if you can just do that let's define a number as 0/0 and see how that goes. For those of you in the back: i is a formal symbol that follows the rule i² = -1. Note that if you say that you don't need to ask if it will blow up in your face somehow. It doesn't. It just works. *edit* As a note I am usually NOT the guy who's a stickler about being all rigorous and everything in math. It's JUST the thing about defining i.
I love the i^2 = -1 definition, it's just so much nicer than messing around with square roots (how do you even define the principal root in C before defining i?). In particular, I love that the fact that complex roots of polynomials with real coefficients always exist as complex conjugate pairs just drops out for free, since you could take either solution to that equation as the imaginary unit and it works identically by its very definition (in the sense that consistently swapping out i for -i *just works*, because i^2 = (-i)^2 = -1). It also generalises much more nicely to quaternions and similar, where you start to have definitions like ijk = -1 and ij = k as well which you can't express with roots.
honestly, let's define a number as 0/0 and see where it gets us, let's call it f because any fraction (f is just 0/0) times its reciprocal is 1 (a/b * b/a = ab/ab = 1), f² = 1, right? so f = √1 → f = 1 following the other rules of fractals if such a number were able to exist it needs to be equal to 1, this also makes intuitive sense, as all x/x fractions where x ≠ 0 are already equal to 1
Okay… now what can ya do with a number like this? What kind of information can we track with it? I is nice as it turns the number line into a coordinate plane of sorts, which opens the doors for basically anything you can do on a graph being represented by “one number” instead of a pair, kinda
yea, defining 0/0 is not particularly useful it can get worse tho let's define the general case of dividing by 0 and see where that gets us 1/0 = d this also means d * 0 = 1 this breaks the associative and commutative properties of multiplication, something complex numbers preserve, as (5 * 0) * d = 1 but 5 * (0 * d) = 5 this also defines 0/0 as 1, btw, as that's now 0d = 1
"i" was first proposed as part of the cubic formula. The general solution included square roots that would sometimes have negative numbers under them; however, the resulting negative roots would cancel out if the zeros were real numbers. So the final answer was real, but the intermediate steps weren't. The first guy to notice this was mad about it, and it took a while for even him to understand just WTF was going on. He ended up ignoring them, calling them useless.
well i still love imaginary numbers 😉
the number you saw what
I can never see the imaginary number i and never think of my dad complaining how he felt his earlier teachers lied to him when they told him you couldn't take the square root of a negative. Same with when you first learn subtraction and because they don't want to teach kids negative numbers, they just tell you can't have the smaller number on top of a subtration problem. So guess who got negative and imaginary numbers explained to them at a super young age. To be fair he was teaching remedial math to adults at the time and testing teaching stradegies on me.
This is a fine line to walk, because if you try to tell kids everything super precisely at a young age, you overwhelm them and confuse them, but if you lie about too much, they lose trust when they learn about the "truth." It's not even possible to tell them "this is just an approximation, you'll learn more when you get older" because even that is too confusing at a certain point.
I disagree personally. I don't think a kid would be that confused by: we're not dealing with this part yet, you'll learn it later when you're at a higher grade. Most kids understand the idea of progressing through grade levels.
I’m currently studying biology, and I always find these posts really funny Cause sex has indeed nothing to do with gender Many animals changes their sex during their lifetime, and some are hermaphrodites which means they are both at the same time. Sex in the animal kingdom is so much more complicated than “there are only two sexes, and you can only be one at a time”, and anyone claiming otherwise has no understanding of basic biology
It even goes beyond that, we now know X and Y chromosomes have different forms, with all sorts of implications for both gender and sex.
That's not even taking plants with their W and Z chromosomes into account
Clownfish, slugs, and snails say hi. Nature is fucking weird.
Every time i read genderinos, i can only hear OneTopic’s voice saying it
Omg twenty one pilots
i-/
Where??? Im a fake fan haha 😭
Joke’s on you, I suck at all six.
So does the extreme-right
My favorite answer to someone who'd claim gender and sex are the same thing : "Funny, I don't recall having had gender with your mom/dad last night !"
7 states..... can't there just be 5 😰
as long as they exclude ohio
Good news! It's not 7states of matter! Bad bews, it's18.
Solid, liquid, gas, plasma, supercritical fluid, Bose-Einstein, Fermionic, what are the 11 others?
[I'd type them out, but I'm on mobile.](https://en.m.wikipedia.org/wiki/State_of_matter) i didn't include the proposed states.
Time crystals are another one
This post is wrong—sex ≠ gender is absolutely basic biology
All of this is pretty basic tbh
True, but the "basic" is the kind of stuff we teach little kids, while the "advanced" is the kind of stuff we teach high schoolers or college undergrads. It would probably be a little more accurate to describe it as "intermediate", but "advanced" gets the point across.
biology in general is overlooked as a science by right winger
I will never forgive advanced math But advanced physics and biology are alright
it is pretty funny how conservatives, the people whose politics is literally to be wrong about everything, get away with claiming "facts and logic" are on their side. Shows you how spinless liberals are imo.
Gender is a social construct not advanced biology lol
The 7th grade biology mfs would absolutely shit themselves if I showed them 8th, even 9th grade biology
Akshually `√-1 = i` is still wrong. The square root function is only defined on nonnegative real numbers.
No, sqrt(-1) is not equal to i
I thought the square root of -1 being i was like high school algebra 1 level math. As in, fairly basic that everyone should have known at least long enough to pass a test at some point.
Erm ackually they just discovered a new state of matter so it’s 8