ITT make mathfags seethe

[Anonymous No.11459644]

Post facts that make mathfags seethe.

I'll start

Let [math]\delta : \mathbb{R} \rightarrow \mathbb{R}[/math] such that:
[eqn]\delta (x) =
\begin{cases}
1 & x = 0 \\
0 & elsewhere
\end{cases}[/eqn]

And most importantly:

[eqn]\int\limits_{- \infty}^{+ \infty} \delta (x) dx = 1[/math]

[Anonymous No.11459647]

>>11459644
Lmao I fucked up.
[eqn]\int\limits_{- \infty}^{+ \infty} \delta (x) dx = 1[/eqn]

[Anonymous No.11459650]

>>11459647
What kind of integral is that?

[Anonymous No.11459653]

>>11459650
A "mathfags get their panties in a bunch when they see it" kind of integral

[Anonymous No.11459657]

>>11459647
why would a function defined this way make anyone seethe? it’s very useful for physics.

[Anonymous No.11459663]

>>11459657
The fuck do I know. Mathfags complain about it because memesure theory or some shit

[Anonymous No.11459664]

>>11459653
Can you define it in a somewhat more formal manner?

[Anonymous No.11459665]

>>11459663
>Mathfags complain about it because memesure theory or some shit
what did he/she mean by this?

[Anonymous No.11459691]

>>11459664
Lebesgue

[Anonymous No.11459695]

>>11459691

nice definition retard

if you want to make a mathfag seethe, just claim a differential is a fraction

watch them fume while they stumble and rage mumble and their head gets redder (or browner if its a pajet)

[Anonymous No.11459704]

>>11459691
But if that integral is in the Lebesgue sense, then it evaluates to zero.

[Anonymous No.11459729]

>>11459664
>Formal
Fuck off with your mathfag buzzwords lmao

[Anonymous No.11459755]

>>11459644
>>11459647
Me? I prefer [eqn] \text{For real } c, \ u_c(t) \equiv \begin{cases} 1 & t > c \\ 0 & t<c \end{cases} [/eqn] then [eqn] \delta(t-c)\equiv\frac{\text{d}u_c}{\text{d}t} \ \ \text{and} \ \ \mathcal L\big \{\delta(t-c)\big\}=\exp(-cs) [/eqn]
where [math] \exp(\lambda t) [/math] is defined to be the solution of [math] x'=\lambda x, \ x_0=1 \ \ \text{for complex} \ \ \lambda [/math].

[Anonymous No.11459758]

>>11459644
You absolute fucking brainlet that's literally like saying "let x=5 such that x=2"

[Anonymous No.11459761]

2+2=4

[Anonymous No.11459776]

>>11459644
No such function exists, so um..

[Anonymous No.11459781]

>>11459776
>drives a golfball 400 yrds
Fell free to describe the force applied to the ball by the club as a function of time without [math] \delta [/math], fucking math nerd lmao

[Anonymous No.11459801]

>>11459781
No such function exists, period.

[Anonymous No.11459802]

>>11459801
*pretends it exists anyway*
*gets useful results*
*shits in your mouth*

[Anonymous No.11459809]

>>11459802
Then you're pretending existence of something different than what OP wrote

[Anonymous No.11459860]

>>11459755
Basado

>>11459758
Lmao seethe more, mathfag

>>11459776
Seethe

[Anonymous No.11459879]

>>11459644
>>11459647
>the integral of the Kronecker delta on the real line is one
>>11459776
>the Kronecker delta doesn't exist

[Anonymous No.11459900]

>>11459879
Such function simply doesn't exist not because it's a distribution rather than function or whatever, but because OP fucked it up. If anything, it should say delta(0) = infinity. Joke's on him.

[Anonymous No.11459916]

>>11459691
brainlet Lebesgue returns 0 to this because it is non-zero on a countable set

[Anonymous No.11460231]

>>11459900
Cant you read retard?

[math]\delta (0) = 1[/math] by definition.

By the way:

[eqn]\frac{dy}{dt} = -ky \\
\frac{1}{y}dy = -kdt \\
\int \frac{1}{y} dy = -k \int dt \\
ln(y) + c_1 = -kt + c_2\\
y(t) = e^{-kt + c_2 - c_1}[/eqn]

[Anonymous No.11460241]

>>11460231
>δ(0)=1
That isnt true though. Not even for engineers.

[Anonymous No.11460243]

>>11459644
>>11460231
>[math]\color{green}{\delta ( 0 ) = 1}[/math]
Actual retard.

[Anonymous No.11460254]

>>11460241
>>11460243
Lmao youre right, im thinking about the discrete delta function

[math]\delta [0] = 1[/math]

[Anonymous No.11460770]

>>11459755
good boy, you finally learned first year differential equations

[Anonymous No.11460777]

>>11460231
delta(0)=inf moron

[Anonymous No.11460798]

>>11460777
Read >>11460254
You fucking imbecile faggot

[Anonymous No.11460806]

>>11459801
No the Kronecker delta isn't a map between the reals.
Yes it is a function in the sense that physishits use the term.
Having a different definition of function that excludes generalized functions doesn't make you smarter just bad at communicating.

[Anonymous No.11461202]

[Anonymous No.11461341]

>>11459644
>Let δ:RRδ:RR such that:
>isn't a map between the reals.

[Anonymous No.11461352]

>>11459695
a differential isn't a fraction though so you're wrong and saying "lol mathfags seethe" doesn't make yo uright

[Anonymous No.11461365]

>>11461352
>A differential isnt a fraction
Lmao but it is, how do you solve something like [math]\frac{dy}{dt} = -ky[/math] then faggot?

[Anonymous No.11461483]

>>11459644
*chad Russian mathematician blocks your path and pioneers distribution theory*

[Anonymous No.11461503]

>>11459644
e^(t*pi*i) = cos(t) + i sin(t) isn't true for quaternions

[Anonymous No.11461552]

>the heaviside distribution

[Anonymous No.11461580]

>>11461365
By treating it as a fraction

[Anonymous No.11461584]

>>11459644
>>11459647
Where can I go to learn the notations used here?

[Anonymous No.11461590]

>>11459644
nice distribution

[Anonymous No.11461604]

>>11459663
Physicsfags complain that mathfags complain about this, but we really don't give a shit what you do.

[Anonymous No.11461613]

>>11461584
A math class. None of these fags are self taught. They're all lonely math majors

[Anonymous No.11461671]

>>11459695
>>11459704
>>11459916
ITT: people who missed the point of the thread

[Anonymous No.11461682]

test

[Anonymous No.11461684]

>>11461613
College isn't an option for me. Is there no other way? A book of notation definitions? A video?

[Anonymous No.11462451]

>>11461671
>I was just pretending to be retarded

[Anonymous No.11462463]

>>11461684
https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

[Anonymous No.11462720]

>>11459644
calculus is like a braindrug.

[Anonymous No.11462729]

>>11459695
dy/dx can be interpreted as a fraction of 1-forms in a way that's mathematically rigorous and even helpful.

[Anonymous No.11463028]

>>11462729
>dy/dx can be interpreted as a fraction
Really? What field does dy belong to?