>Dirac delta """""""""""""""""""function""""""""

>>7952590
Looks like a function to me m8

>>7952590
this is even addressed on the first line of the fucking wikipedia page

low quality b8

>>7952693
""""""""""""""""""""""""""""b8""""""""""""""""""""""""""""

>OP is """"""""straight""""""""

>>7952590
I've only ever seen physics students and expert memeologists sperg out over this.

>>7952723
>physics students
>memeologists
>NOT THE SAME THING

LE BAZINGOOOOOO XDDDDDDDDDDDDDDD

>>7952635
A function can't be almost everywhere zero and have a non zero integral, dumbass

>>7952702
I'm willing to get fucked in the ass if that's what it takes to stop this out of control function

>>7952747
>l2measures

>>7952723
But physicists are the ones who use it as a function and refer to it as such.
For example, the QFT book I'm reading said that a particular element of the scattering matrix was some function times [math]\delta(0)[/math]!
A physicist will define the functional derivative the same way you'd define a normal one, but with a delta function in place of the coordinate difference delta-x, which is very simple but the functional you started with was only defined on functions, not distributions!
A mathematician would introduce some new machinery and say the functional derivative is the Radon–Nikodym derivative or Fréchet derivative or whatever.

>>7953516
>[math]\delta(0)[/math]!
I don't mean the factorial of [math]\delta(0)[/math], by the way - that would make even less sense.

>>7952590
>he doesn't know distribution theory
>he thinks the Dirac is the only "function" to be like this
To be fair, everything would be simpler if we'd just go with non-standard analysis

>>7953529
everything would be simpler if we stick to ultrafinitist math.

>>7953531
It really wouldn't.

>>7953500
What are you talking about? Is there some way to get area out of purely length?
>inb4 space filling curves

>>7952590
Why don't we just call it Dirac delta measure or Dirac delta limit?

>>7952590

If highschool math was bad, then jumping to college level math would equally cause you to """""""""""sperg out""""""""""".

The dirac delta is not a function but a functional,
a linear function of functions. The distribution theory guy earlier pointed in this direction.

And is it useful? Damn right, differential equations wouldn't be the same without this """""""function"""""".