>There's no such thing as the perfect func-

>>8876405
>Dirac delta
>function
>>>/lgbt/

>>8876534
>Dirac
It's Kronecker you mongoloid chemistry major.

>>8876534
Please tell me this was your pathetic attempt at trolling and not a serious comment

>>8876681
as the thread, so the post.

>>8876405
Kronecker is based tbqhf

>>8876534
Explain how the Dirac delta is not a function.
It's differentiable and it's integrable, a range and a domain.

>>8876820
it's not a real-valued function, and if you extend the range to include a formal infinity to make it a function you can't apply the majority of the theory you have about real functions

at least read the wiki page which before spouting off such nonsense

>>8876831
So basically, it's a function.

>>8876534
>>8876820
>>8876831
Since it's a linear functional, it is a real valued function, but it's domain is a space of functions. That is, if we're talking about the theory of distributions.

It can be defined as an internal function R* -> R* (the hyperreal field) or as an equivalence class of Cauchy sequences in some appropriate function space.

But it is not a function in the usual sense, and that's what I think he meant.

>>8876838
>So basically, it's a function.
actually it basically isn't

if you want to learn the basics about distributions there's even MOOCs for it
https://www.coursera.org/learn/theorie-des-distributions/

>>8876405
[math] 1+1 = 0[/math]

it's a function

>>8876872
>and that's what I think he meant.
I admit was shitposting, but I'm kind of surprised that anons came to vehemently defend the Dirac Delta being a function. What level of irony is this?

A function is just a subset of the Cartesian product of that is a relation and every "x" maps to just 1 "y". It's just not a real valued function and you cannot just operate it as a real valurd function without proper considerations.

>>8877001
*Of two sets.

>>8877001
Tot clarify, diract delta is a function, just not a fuction that goes from R to R. I don't know why mathematicians love to say it's not a function when I think many people who has taken some set theory understands that there are other types of functions.

>>8877018
>I don't know why mathematicians love to say it's not a function when I think many people who has taken some set theory understands that there are other types of functions.
because an entire field of mathematics had to be developed to deal with these kinds of "functions"", this work was important enough that people got fields medals for it, it's not just a trivial re-understanding of the word function...

>>8877018
Well, most engineers use it in R<->R context, just under integrals, hoping that no one notices.

>>8877001
>uses terms like "x" and "y"
>expects to be taken seriously

>>8877027
It's still a weird way to correct people considering that a space of functions is not such an abstract concept if you have taken linear algebra. And if you have, you probably know about the dual space and all that shit that still relates to functions. My teacher never said that a functional isn't fuction, but when I mentioned Dirac's delta he specifically said it wasn't a function which was really weird. Obviously the correction comes from engineers and physicists using it as a real valued fuction without proper consideration, but I just find it weird that they don't say something such as "It's not a real valued function though, but it's a function from a fuction space to the field" and tada.
>>8877030
I'm a mathematician and my professors still told it like that.
>>8877048
I'm not going to write it in formal symbols faggot. It's clear what I mean.

>>8876405
it's just an indicator function

>>8876872
If you're going to be pedantic about it, then the Dirac Delta really isn't a function, even in this generalized sense. You're conflating the distribution [math] \delta(f)=f(0)[/math] with its (non-existent) Radon-Nikodym derivative, which is the "function" [math] \delta(x)[/math] defined by Dirac. It's like the saying that the number 1 is the function that maps every compactly-supported integrable function f to [math] \int_{\mathbb{R}} f(x) dx[/math].

>>8876831
It is a real valued function if you interpret it as a measure.

>>8876996
You weren't shitposting. You were a fucking dumbass and got called out on it.