What's something math related that confused you for a while but soon made sense in a moment of clarity?

Nigga N is infinite but you can still count dat shit, real talk ma nigga

I didn't group all infinite together though, i said sets are either finite or infinite, that doesn't entail that there aren't infinite sets larger than other infinite sets for the same reason saying sets are finite doesn't entail some finite numbers aren't larger than other finite numbers.

BTFO

Nice one Op.

Pythagorean theorem, I saw a proof of it with a square and it made a lot of sense

but we're talking about cardinalities, where the vast majority of the interest in studying them comes from the intricacies and counterintuitive results that come from having a variety of infinities, like the continuum hypothesis, space-filling curves, etc... saying 'a set either has a finite number of elements or an infinite number of elements' misses the point of cardinalities entirely

cantor's work wasn't controversial for nothing, whether it was important mathematicians like kronecker who literally didn't believe his results or philosophers like wittgenstein who dismissed his work entirely

You sound confused.

infinite sets, functions, real numbers and angles in trigonometry are problematic concepts which can't be taken for granted.

Group Actions

I was actually drunk as shit

limsup made more sense to me when i saw the definition that says limsup is the supremum of the set of cluster points.
can you explain that shit to me user. i still dont fully get it.

the differences between pilot study and pretest in psychological research

>your a brainlet
>your
The irony

Factoring. I skipped class when we were learning it and was confused as fuck by it until I got to college.

nothing confusing about this

that's not confusing

This and the reason why pi is 3.14...

that's sad

>addition is commutative until you add too many things together xD

addition is commutative no matter how many things you add. you can't add an infinite number of things

a gorup action is just a group element acting on something. what's so hard about that

Laplace Transforms. I blame the EE order of Laplace Transforms -> Fourier Series -> discrete/continuous Fourier Transforms -> Z Transforms.

This for me too. In HS, whenever the factoring of polynomials came up, the teachers all acted like it was something you were just supposed to "see". I took until first year undergrad until I learned that all you need to do is find the roots of the polynomial.

Lagrange Polynomials

Mathematical Induction

P=NP

Finally figured that shit out!

u substitution

Care to share the proof for us all to see?

This has to be bait.

Banach–Tarski paradox

>just kidding I still don't understand it

is quite simple

u l r d d l u r u d u l r d r l u d r r u l u d r

now there are two balls

just think of it like mitosis

How the fuck is that confusing?

How to look at a differential equation and how to realize what method to use without going through EVERY method (would take forever on an exam)

took many Ds and Cs on exams/quizzes and long sleepless nights of deciphering the book to finally figure it out

The sum of all primes is -1/12

To put it roughly, you take all the constiuent elements of a ball and then manipulate them such that they make up a whole nother ball

i dont get the homorphism definition.

Stoke's theorem, mainly the concept of curl in R3

Grassmann numbers (currently doing QFT)

Why the fuck is the derivative and the integral defined the way it is and why are they the same??

Mind sharing what you figured out?

Equivalence classes. But I think it had a lot to do with not understanding the definition of the notation.

Homological Algebra. Shit is so abstract.

One-time pad decryption

This

epsilon delta proofs
wat

I still can't visualize what a curl is.

Decrypting One-time pads.

oh i thought you said one-time pad encryption, my bad.

Will integral calculus ever not fuck me around?
How are people good at it? Are they just very smart?

>mfw brainlets get confused about things
Such plaebeians, unlike enlightened gentlesirs such as myself.

take a wheel/turbine/fan and place it into the vector field at the point r. does the wheel start spinning? if so, there is a non-zero curl at the point r

>Also what the fuck are these long-legged, green characters I keep seeing posted here?
kek idk either, is it from a cartoon or something?
maybe those books like pic related?

Practice makes perfect, user

I was always a straight A student in math but the only topic I struggled with was Volume by Revolution
I got a 100 on each test except for the one with the volume question because the cross section stuff didn't make sense
Though after summer break and coming back to school it's so intuitive and second nature and feels good

A turbine and a fan will spin in a velocity field of all parallel, unidirectional vectors - if placed perpendicular to them.

injectivity, surjectivity and bijectivity.

it is if you interpret it as an actual sum and not a limit

>me too
FUUUUCK I'm such a disgrace

what made it click?

>currently stuck, probably has something to do with my terrible algebra skills

i second this, lets help each other because we're all on Veeky Forums together

mind sharing?

>went over it last week in class, still have no idea other than it's vaguely connected to power sets, except you just start making the power sets at whatever element you want to make an equivalence class for

how can you be so fucking stupid to miss the irony in the post you are replying to? Or am I being reverse trolled?

BLOWN
THE
FUCK
OUT

The definition of a limit in category theory. Feels so good now though.

y=ax + b
being translated by

And also differentiating more than once, when I learned about image processing and how rate of change applied recursively makes sense. Or at least a tiny bit, I am a bit confused still, but differentiating once and twice is not magic to me anymore.

The covariant derivative.

I was so hyped about them when I first saw them

Not him, but think of a ladder

How do you know you can climb a ladder?

Well, first you have to know if you can climb on to the first step from the floor

Now, imagine you're mid ladder. Given that you were already able to get to the middle of the ladder, can you climb onto the next step?

Since we've shown we can climb the first step, and that if we're mid ladder, we can climb onto the next step, then this shows we can climb onto the second step. But in turn this means we can climb onto the third step, etc.
So to prove sum of integers is [math]1+2+3+...+n=\frac{n(n+1)}{2}[/math], we first have to show we can get onto the first step. The sum of the first integer is [math]1[/math], and [math]\frac{1(1+2)}{2}=1[/math], so we got onto the first step.

Now imagine we can climb onto the [math]n[/math]th step, ie: we know for some [math]n[/math], that [math]1+2+3+...+n=\frac{n(n+1)}{2}[/math]. So [eqn]1+2+3+...+n+(n+1)=\frac{n(n+1)}{2}+(n+1)=\frac{n^2+n+2n+1}{2}=\frac{(n+1)(n+2)}{2}[/eqn]
Which is the same as [math]\frac{n(n+1)}{2}[/math] but with [math]n+1[/math] instead of [math]n[/math]. So if we're on the [math]n[/math]th step, we can climb onto the [math](n+1)[/math]th step. So if we're on [math]1[/math], we can get to [math]2[/math], so we can get to [math]3[/math], etc...

will it though

okay so you just substitute n+1 for n, then manipulate the equation algebraically until it looks like the LHS?

pretty basic shit and not really as much understanding anything as noticing redundancies in some formula listings

[math]ln(\frac{x}{y}) = ln(x\frac{1}{y}) = ln(x) + ln(y^{-1}) = ln(x) - ln(y) [/math]

puttin this man into retirement god damn

yeah, but also works for inequalities, integrals, divisibility,etc

innie dash outie dash innie

the chain rule

f'g + g'f

faggot + his gf

product rule

>the faggot and his gf

bump

le margarine is twoo smol xdddd