/sci/ - Science & Math » Thread #13811189

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This kills the physishit

Anonymous Tue 02 Nov 02:01:24 2021 No.13811189 View Reply Original Report

Quoted By: >>13811310 >>13811490 >>13812952 >>13813058

Dirac delta functi-

Anonymous

Anonymous Tue 02 Nov 2021 02:19:02 No.13811227 Report

Quoted By: >>13811420 >>13812685 >>13813207

imagine getting filtered so hard by measure theory you whine about it for the next decade on an ukrainian ascot monogramming forum lmao

Anonymous

Anonymous Tue 02 Nov 2021 03:02:42 No.13811310 Report

Quoted By: >>13811333

>>13811189
I'm pretty sure you can define it with codomain being something like $S\vee \mathbb{R},$ where $\infty\in S$ connects to $0\in\mathbb{R},$ and then define a fairly natural integration, and manage to make all the integration properties work as expected.
Someone correct me if I'm wrong.

Anonymous

Anonymous Tue 02 Nov 2021 03:11:50 No.13811333 Report

Quoted By: >>13811391 >>13811490

>>13811310
Consider
$\alpha = 2 \delta$
If $\delta$ is 0 everywhere except 0 and infinity in 0 then clearly $\alpha$ is too but
$\int_{-\infty}^{\infty} \alpha(x) dx = 2 \int_{-\infty}^{\infty} \delta(x) dx = 2$

Anonymous

Anonymous Tue 02 Nov 2021 03:36:35 No.13811391 Report

Quoted By:

>>13811333
For a real number $t,$ write $t_{\mathbb{R}}\in S\vee\mathbb{R}$ and $t_S\in S\vee\mathbb{R}$ to distinguish them, where $S\vee\mathbb{R}$ is defined as above. Then define $\delta(0)=1_{\mathbb{R}}$ and define multiplication on $S\vee\mathbb{R}$ naturally, i.e. for any $t,u\in\mathbb{R},$ we have $u\cdot t_S=(ut)_S,$ and $u\cdot t_\mathbb{R}=(ut)_{\mathbb{R}}.$
The integral can then be defined (loosely) as follows: where the function is in $S\setminus\{\infty\},$ take the usual integral, and then add to it the sum of the elements that are in $\mathbb{R}$ of the codomain.
In this way, we'd have $\int_{\mathbb{R}} \delta=1,$ and $\int_{\mathbb{R}} \alpha=2.$

Anonymous

Anonymous Tue 02 Nov 2021 03:50:08 No.13811420 Report

Quoted By: >>13812685 >>13816400

>>13811227
Actually meant to encourage measure theory. There's still a lot of scientists who still call it a function, hell you can google it right now and get booklets calling it Dirac delta function and yet no reference to extended real number line nothing.

Anonymous

Anonymous Tue 02 Nov 2021 04:24:07 No.13811490 Report

Quoted By: >>13811640

>>13811189
physishit here, how will I ever recover?
>>13811333
You're just using the definition of the dirac delta. It's not actually a function but a generalised function (or a GNU/Function as I've come to call it).

Anonymous

Anonymous Tue 02 Nov 2021 06:08:02 No.13811640 Report

Quoted By:

>>13811490
i'd just like to interject, the GNU dirac delta properly occurs inside an integral. thank you

Anonymous

Anonymous Tue 02 Nov 2021 16:25:28 No.13812685 Report

Quoted By:

>>13811227
>>13811420
based measure bros dunking on filtered physishits

Anonymous

Anonymous Tue 02 Nov 2021 16:30:35 No.13812700 Report

Quoted By:

It is a function you morons. It's just a function from the space of continuous functions to the field of scalars

Anonymous

Anonymous Tue 02 Nov 2021 16:37:13 No.13812718 Report

Quoted By: >>13812732 >>13813072 >>13813150 >>13813172

What is this thing saying? There doesn't exist any function in X × Y where F(x) = y for all (x, y)?

Anonymous

Anonymous Tue 02 Nov 2021 16:42:49 No.13812732 Report

Quoted By: >>13812916 >>13813072

>>13812718
for all x in X, there exists a unique y in Y such that (x, y) belongs to f.

Anonymous

Anonymous Tue 02 Nov 2021 16:58:48 No.13812784 Report

Quoted By:

i love delta i love delta i love delta i love delta !!

Anonymous

Anonymous Tue 02 Nov 2021 17:41:09 No.13812916 Report

Quoted By:

>>13812732
Ohhhh I get it

Anonymous

Anonymous Tue 02 Nov 2021 17:49:02 No.13812952 Report

Quoted By: >>13814472

>>13811189
Any book that teaches Maths in English because this gibberish symbol shit makes no sense to me.

Anonymous

Anonymous Tue 02 Nov 2021 18:27:34 No.13813058 Report

Quoted By: >>13813203 >>13816400

>>13811189
It's not a function. The Dirac Delta is a functional or distribution

Anonymous

Anonymous Tue 02 Nov 2021 18:33:33 No.13813072 Report

Quoted By: >>13813150 >>13813172 >>13813203

>>13812718
Yeah it confused me as well
>>13812732
So in this case, does the ! mean "unique"? I'm unfamiliar with that notation and I assumed it means "does not exist" and I got confused.

Anonymous

Anonymous Tue 02 Nov 2021 19:00:17 No.13813150 Report

Quoted By: >>13813172 >>13814448

>>13812718
>>13813072
>>>/g/

Anonymous

Anonymous Tue 02 Nov 2021 19:11:29 No.13813172 Report

Quoted By: >>13814448

>>13812718
>>13813072
>>13813150
I don't understand the confusion, op statement is perfectly clear to me and I am an engineer. Why do the anons that didn't understand it need to fuck off to /g/?

Anonymous

Anonymous Tue 02 Nov 2021 19:23:48 No.13813203 Report

Quoted By: >>13814448

>>13813072
>So in this case, does the ! mean "unique"?
Correct

>>13813058
A functional is also a function

Anonymous

Anonymous Tue 02 Nov 2021 19:25:39 No.13813207 Report

Quoted By:

>>13811227
>ukrainian ascot monogramming forum lmao
kek

Anonymous

Anonymous Wed 03 Nov 2021 03:31:35 No.13814448 Report

Quoted By: >>13814477

>>13813203
Thanks
>>13813150
What? I've never seen that notation in any book.
>>13813172
Because ! meaning NOT is a more or less standard convention in programming languages, and /g/ is the board for brogrammers

Anonymous

Anonymous Wed 03 Nov 2021 03:44:37 No.13814472 Report

Quoted By:

>>13812952
They pretty much all do. It's just written in that way for succinctness.

Anonymous

Anonymous Wed 03 Nov 2021 03:47:08 No.13814477 Report

Quoted By: >>13814479

>>13814448
Maybe because you've never seen a set theory or math logic book? That notation is standard.

Anonymous

Anonymous Wed 03 Nov 2021 03:48:53 No.13814479 Report

Quoted By: >>13814483

>>13814477
>set theory
Cringe
>math logic
Who even cares about this? I'd rather count beans or watch paint dry. Basic truth tables and de morgans laws all a man needs. Anything else is sinful and indulgent

Anonymous

Anonymous Wed 03 Nov 2021 03:50:19 No.13814483 Report

Quoted By: >>13814504

>>13814479
You said you've never seen that notation. I gave a possible explanation for why. There's no need to sperg out. You really do seem to belong in /g/.

Anonymous

Anonymous Wed 03 Nov 2021 03:58:34 No.13814504 Report

Quoted By: >>13814508

>>13814483
I don't belong anywhere.

Anonymous

Anonymous Wed 03 Nov 2021 03:59:31 No.13814508 Report

Quoted By: >>13814529

>>13814504
Then get some rope, faggot.

Anonymous

Anonymous Wed 03 Nov 2021 04:06:28 No.13814529 Report

Quoted By:

>>13814508
Not today. Not just yet.

Anonymous

Anonymous Wed 03 Nov 2021 13:18:25 No.13815337 Report

Quoted By:

Dirac delta is the biggest midwit filter in math, directly followed by treating dx/dy as a fraction.

Anonymous

Anonymous Wed 03 Nov 2021 21:26:39 No.13816400 Report

Quoted By:

>>13811420
>>13813058
Paul Dirac called it a function, and that's good enough for me.

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