/sci/ - Science & Math

1 + 2 + 3 + 4 + ... = -1/12

e^{iθ} = cos(θ) + i*sin(θ)

1 + 1 = 2

Everything else follows from that

>>11925814
What you wrote is not what is written in your pic. I hope you understand that

>>11925814
Are there any functions that can compete with the chad theta functions?

[math]f'(x) = \lim_{h \to 0}\frac{f(x+h)-f(x)}{h}[/math]

Not really a rule, but I like how it can be visualised.

>>11925814
Axiom of choice
>tfw 25 yr old choosier
>choose choose choose
>from any nonempty set
>YES
>im choooooooosing oooooooooooooshiiit

a=a

>>11926014
Can this be graphed?

2 + 2 = 5

>>11926056
Careful there Winston, what did I tell you about posting on wrongthink sites

>>11925814
As a physicist, I think there's nothing quite as elegant or useful as series expansion.
[eqn]f(x) \approx \sum_{n = 0}^{\infty} \frac{{f}^{(n)}(0)}{n!}~x^n[/eqn]

>>11925823
t. first semeser undergrad

>>11926049
Based

>>11925823
The classic.

>>11926055
Did it for a random function, red is the function difference over h with darker shades indicating smaller values of h, the thick blue curve is the actual derivative. It's also easy to wrap your head around since it's basically taking the definition of slope (rise over run), generalizing it to apply to an entire function, and then taking the limit where run goes to zero.

>>11926067
That's an equal by definition of the infinite sum.

>>11925823
This is so meta for /sci/ at this point

>>11926334
Fair enough, I'm used to it being an approximation since we generally stop at first or second order for most shit.

>>11925835
Fuck you: 0 is a natural number if there is an element “n” in the set of natural numbers it contains it’s successor “n+1”

Everything follows from that

>>11926014
This degenerates for multiple variables

>>11925814
In Danish that's known as the idiot formula, because even an idiot can remember it.

>>11926049
Based but bluepilled
>>11926067
Retard do away with the infinity symbol or add a bound

I just like the pythagorean theorem. Simple, can be easily visualised or proved in practice, and it's an inside joke among my close friends.

My favorite rule would have to be
Every open ball is open

>>11926350
Can you visualize it for me in dimensions greater than 3

>>11926334
>every function is analytic
nope

>>11926358
> sweats in didn't do math past highschool

>>11926350
uhhhh
bros?

>>11926375
wtf is this real

>>11926380
No, it's imaginary

>>11926375
This is why we don’t use the standard inner product for complex vector spaces

>>11926391
Symmetry's a bitch.

>>11925814

>>11926375
OY VEY SHUT IT DOWN

>>11926049
this

3^(3i) = -1

0.999... = 1 is a good one

[math]|\mathcal{C}| = \mathfrak{c}[/math], where [math]\mathcal{C}[/math] is the Cantor set.

https://invidio.us/watch?v=Dri2r2jKGes

the age-old equation

[math]|\mathbb{N}| < |\mathbb{R}|[/math]

[eqn]\mathbb{T}\cong \mathbb{R}/\mathbb{Z} [/eqn]

[math] f(a)=\frac{1}{2\pi i}\oint_\gamma \frac{f(z)}{z-a}dz [/math]

>>11926049
based reflexivitychad
>>11926067
>[math]\approx[/math]
>[math]\infty[/math]
>>11925814
[eqn]
\mathrm{succ}(n) = \lambda f. \lambda x. f(n (f (x))) \\
0 = \lambda f. \lambda x. x \\
1 = \mathrm{succ}(0) \\
2 = \mathrm{succ}(1) \\
\vdots
[/eqn]

>>11925814

>>11926375
You'd usually define the metric of a 2d euclidean complex space by [eqn]
ds^2 = dz d\bar{z}
[/eqn] i.e. the distance between two points on the complex manifold is [eqn]
\int \sqrt{dz d\bar{z}}
[/eqn] then the distance between the points (0,1) and (1,0) in the complex plane (i.e. i and 1 respectively) is just [eqn]
\sqrt{(1-i)(1+i)} = \sqrt{2} [/eqn]

P({{}})={{},{{}}}

Incredible

>>11925814
[math]e^{a\partial_x}f(x)& = f(x+a)[/math]

>>11925814
1+1=2

>>11926056
>>11926066
samefag

>>11926375
Recall in the complex plane the generalized Pythagorean theorem as,

|a|^2 + |b|^2 = |c|^2

The absolute value is defined as the distance from the origin, which is 1 for both 0+1i and 1+0i. Making the hypotenuse root(2)

>>11929506
Since |x|^2 = -1 doesn't have a solution in the complex plane, I'm just going to invent a new number "h", a "hallucinatory number", which does satisfy the equation.

Now replace the i in the diagram with h.

>>11925814
>math rule