# It's a function

cum2soon

it's a function

Attached: 1200px-Greek-lc-delta.svg.png (25 KB, 1200x1200)

Inmate

It is.

idontknow

filters are not functions

Gigastrength

it's a function
Who are you quoting?

PackManBrainlure

Emberfire

distributions are generalized functions (so all functions are distributions, but not vice versa)

Flameblow

What us your definition if a function?

VisualMaster

It's a measure over $\mathbf R$.

Garbage Can Lid

whom*

Boy_vs_Girl

Neat, infinitesimals are intuitive and explain everything.
"n-no goy, you need to use these nonsensical limits that say the same thing but make it fifty times more convoluted!"
Whoever came up with and supported this limit bullshit should be rounded up and sent to prison camps.

haveahappyday

whose domain is a function space

massdebater

It is the great filter for brainlets

LuckyDusty

What is a generalised function?

ZeroReborn

whose*

TechHater

It's just a linear functional, that is, a function. Fucking amerimutts after their silly """""""""""""calculus""""""""""""" courses thinking only $\mathbf{R}\to\mathbf{R}$ are functions, and any other map must be some spooky "generalised function"

BinaryMan

Moron.

It's a function $\delta: \mathbb{R} \times \mathbb{R} \to \{0,1\}$
[eqn]\delta_{ij} = \begin{cases}
1,& \text{if } i=j\\
0,& \text{if } i\not=j
\end{cases}[/eqn]

Emberburn

whoms't'eds*

SniperGod

Attached: 5bb.gif (1.08 MB, 279x219)

SniperWish

That's not what $\delta$ means.

King_Martha

He doesn't know about the Kronecker delta

Calclets get out.

PackManBrainlure

and measures are "set functions" so it is a function

Burnblaze

based kronecker master race

Soft_member

RavySnake

He means the Dirac delta, the continuous analogue of the Kronecker delta.
It is you who needs to get out.

RumChicken

it's a function
She's a liar. You are a literal god at that IQ stage.
My friend literally learned Calc 4 material DURING the final and ended up acing it. He didn't even know there was a final this day and entered in the room by mistake. He's in the 120 range. He ended up with a A++ in the class but got expelled anyway because he wasn't even registered at this uni.

Supergrass

the unit impulse response function isn't a function
are you guys fucking stupid or something?

Lord_Tryzalot

Wanna know how I know you're lying?

Fuzzy_Logic

go for it you fucking brainlet

Spamalot

Who was student? Albert Einstein.

New_Cliche

why is the dirac delta function not a function

Illusionz

It's a reproducing kernel

Poker_Star

Yes, but that way it never equals infinity.

Boy_vs_Girl

I don't know. Why can't it just be a non-analytic function?

iluvmen

What do you mean by that? Measure is a function on some family of sets that admits values from range $[0,\infty]$, or $[-\infty,\infty$ if we don't require it to be positive

Poker_Star

$[-\infty,\infty]$ obviously

BinaryMan

He means the Dirac delta, the continuous analogue of the Kronecker delta.
Why would he (assuming OP is a "he") mean that?

Emberburn

Define $\delta: A\,\longmapsto\,\mathbf 1_A\left(0\right)$ and replace $\int_I f\left(x\right)\, \delta\left(x\right)\, \mathrm dx$ with $\int_I f\,\mathrm d\delta$. Same as having $\delta\left(0\right)\ =\ \infty$ but less handwavy.

Evil_kitten

Who says it's a function? That's just plain stupid.

Clearly it's a functional, for variance.

Nude_Bikergirl

And how are functionals not functions?

iluvmen

is it not a state change function?

kizzmybutt

Feel free to use hyperreals, nobody is stopping you user-kun

TreeEater

Because people always meme about the Dirac delta "function"

Sharpcharm

They are, but not from reals to reals
They are functions in the same sense that covectors are functions. They're functions that are defined over function spaces, that is they take a function as input and THEN get a real number as output. The interpretation that Dirac delta is a function R->R is just a handy interpretation that intuitively works but is wrong strictly speaking. Just like most of distribution theory, which is just a bunch of formalisms that legalise physicists' intuitions.

Burnblaze

Because the Kronnecker delta is a function, from Z^2 to {0, 1}. And is not memed about.
Welcome to the real world, where context (including societal context) matters

Evilember

$$f(x) = \pm\sqrt{x}$$
Its a function, prove me wrong, niggers.

RavySnake

Since my first semester of undergrad, my definition of function was correspondance between sets that's uniquely defined, so the clarification is not needed, and to be honest, the functional itself is used by physicists mostly for compact notation or to skip formalism in QM. The only relevant part are green functions.

VisualMaster

thist

JunkTop

I wonder if any of you retards ever actually went through theory of distributions. Fucking kek, I'd be even surprised if majority of mathfags prowling this site did.

You're all small-time

Crazy_Nice

Yes. As I said, technically speaking it IS a function, but when people talk about functions they usually mean "regular functions", that is, functions that map a number set to another, not things like Schwartz space covectors. It's like saying "The Earth is not spherical" - while technically it's closer to an oblate spheroid and you are technically correct, people assume what you mean to say it's flat.
And likewise when you say "function", you intuitively mean from R^n or C^n to R or something, not from Schwartz space to R.
There is a reason those have a specific name for them in order to differentiate them: "functionals".

How the fuck would we not? It's literally Calculus III, so second year of physics/astronomy at my Uni
I assumed anyone who has used the Dirac delta (that is to say, anyone who has QM, because that's where it appears), would be taught basic distribution theory
t.

massdebater

Physicists most of the time do have analysis class that covers distributions, but I've heard from most math students that undergrad doesn't even cover PDEs in required courses, so I'd be surprised if they even did distributions theory, since you can't really build PDEs without it.

Playboyize

desu I highly doubt that distributions are part of most Calc 3 courses, they end up with surface integrals most of the time, in good unis with differential forms.

Emberfire

For me, it was:
Calc 1: from the definition to naturals based on an empty set to single-variable integral calculus
Calc 2: multivariable diff and integral calculus, beginning of differential geometry
Calc 3: more diff geometry, complex calculus, sprinkled with distribution theory
Calc 4 (optional): partial differential equations
University of Warsaw, for reference

BlogWobbles

Engineers use the Dirac Delta a fuckton and are certainly not taught distribution theory

RumChicken

Where is measure theory, ODEs, calculus of variations, metric spaces, series, differential forms, integral transforms ???

Fuzzy_Logic

measure theory
There is not
ODEs
calculus of variations
...what?
metric spaces, series, differential forms
Calc 1
integral transforms
If you mean Fourier transforms, also Calc 3 (as the final part of complex calc). Otherwise there was none
Basically Calc 1-3 was a speedrun to cover everything we need for QM during the 4th semester.
And that's it for compulsory mathematics
Yep, PDEs are optional during undergrad physics here
Right, I forgot engineers. My bad

Boy_vs_Girl

Fugg I want this.

They are, but not from reals to reals
Yes, they are, and that's enough. Maps $\mathbf{R}\to\mathbf{R}$ aren't better than maps between arbitrary sets. If you say Dirac delta isn't a function $\mathbf{R}\to\mathbf{R}$ then it's true, but when retards say it's not a function but some spooky generalised function (without defining what the hell does that even mean) that's just beyond retarded

What the fuck, at University of Warsaw third and begining of fourth semester of analysis is measure theory, differential forms and complex analysis is not introduced untill analytic functions, which you take during 5th semester (and which wasn't mandatory untill this year if I'm not mistaken)

TreeEater

Where is measure theory
Third semester of analysis
ODEs
There is a course called ODEs, usually taken during 4th semester
calculus of variations,
Im not sure, really
metric spaces
Topology and third semester of analysis
series
Numerical series are first semester of analysis, functional series are the second
differential forms
Fourth semester of analysis
integral transforms
Analytic functions or functional analysis, 5th or 6th semester

eGremlin

This seems okay, except for lacking calculus of variations

This is absolutely not okay and your school is really shit.

AwesomeTucker

Differential forms in Calc 1

I seriously doubt that you were learning about generalized stokes' theorem in Calc 1 bruv

PurpleCharger

It's a function $\delta: \mathbb{R} \to \mathbb{\overline R}$

Supergrass

How does

$\int_{-\infty}^{\infty} f\delta \mathrm{d}x = f(0)$

make sense with this definition though?

I'll save you the work, it doesn't. That's why Schwartz had to create a whole new theory to make it work.

Ignoramus

Cf.

TreeEater

Then what function is $2\delta$?

Actually, $\delta$ IS a function, but not on $\mathbb{R}$ but on a space of test functions.

By the way - OP gave us a trick question. $\delta$ is just a Greek letter.

Boy_vs_Girl

I'm talking about Faculty of Physics which definitely has complex calc during the 3rd semester because I just finished it last semester. It's all a lot slower at the Faculty of Mathematics, where you don't have to speedrun through all the things you need for QM so you can take your time
Oh fuck, I confused the names because I'm Polish and the course language was Polish. Diff forms were between 2nd and 3rd semester, as part of diff geometry.
It's the best one in my 2nd world country.
No idea how good or bad it is related to the unis abroad

haveahappyday

Pretty sure Abraham Robinson was Jewish, but okay.

takes2long

Diracs deltas have nothibg to do with infinitesimals brainlet.

RumChicken

So it's the discrete metric but backwards? What's it used for?