Ridiculous Notation and Conventions

They're pretty understandable/concise when you're used to it, but lots of notations/symbols used in standard QFT gets pretty wild.
>Dirac delta
>kronecker delta
>functional derivative
>variation in a function
>delta as a variable itself
>implicit indices on virtually symbol you write down, typically several kinds of contractions implied by juxtaposition of symbols.

Are you retarded?

Do you understand that division is defined in terms of multiplication? You can do them in any order because multiplication is associative.

[math]\frac{a}{b} \equiv a \cdot b^{-1}[/math]

Have you ever heard of the distributive law?

[math]a \cdot (b +c) = ab +ac[/math]

If you want to have precedence order to save your hand from writing parens, distribution pretty much makes the choice of operation order obvious.

When you rely on stupid mnemonics to understand rather than just plain ole understanding, you tend to show your lack of understanding. Understand?

Of course you can multiply functions. You sound sad that composition and multiplication are two different things. Why?

Composition:
[math]f(g(x)) = h(x)[/math]

Multiplication:
[math]f(x) \cdot g(y) = h(x,y)[/math]

You are literally retarded.

When you have f:A->B,
f is a function
f(x) is a function evaluated at x (it is an element in the image of the function.

(f*g)(x) is syntactic sugar for f(x)*g(x). You are never multiplying the functions themselves, only elements in their images. Furthermore, it only makes sense when there exists a multiplication in the codomain and both functions share the same codomain.

For instance I can have continuous functions between topological spaces without algebraic structure (no addition or multiplication).
f:A->B
g:C->D
Then what the fuck is f*g?
What the fuck is f(a)*g(c)??

There is a different notion called a categorical product but in the context of category theory exponents always refer to composition and inverse.

he's dug himself into a semantic hole after getting irrational upset at the idea of sin^2(x) popping up all over the place in virtually every field of science and existing as a well-understood/agree-upon notation.
I wouldn't worry too much, friend.

i never said multiplication between any two functions is always defined

it is still multiplication of functions

you are attempting to be a pedantic brainlet and failing

No it's not. Multiplication of functions would give you a new function. Multiplication of elements in the image is just that.

Suppose
f:A->B
g:A->B
h:C->D

Then fill in the question marks
f*g:?->?
f*h:?->?

You are using a lot of big fancy words there, bob.

Tell that to /b/. When it comes to math, some of those guys are fucking retarded.

when you multiply, for example, polynomial functions, you get a new polynomial function

When people use "~" to mean "is proportional to" and "is approximately". My prof in statistical thermodynamics used to do that and it drove me nuts. Especially since there are alternate notations you can use for both that can't be misinterpreted.