Mathematics

$\int dF$ doesnt mean anything though

@Faust Of course it does, just as $\int{dx}=x+C$

for example let $dF(x) = 2x$

god, this discussion is cancer

2

i Come here to laugh at you all

11:03 PM

You're not any better

then your saying $\int 2x dx = \int x^2? $ or your saying $\int 2x dx = \int 2x $ but the $\int 2x = 2xy$ or $ x^2 ?$ what your writing down is nonsense

@Faust Why is your differential not written with respect to another differential

Am not better , am not even on the same axis

right, these guys at least have hope of doing something good

@Faust What?? I never said you can have an integral sign without a differential

$dF$ is a differential!

11:05 PM

idk What good they want to do but they sure are going about it the wrong way

Unless by good you mean someday write a math paper that nobody is gonna read

What are we fiting about

@BalarkaSen Tell me if this is logical

5 mins ago, by Sir Cumference

25 mins ago, by Sir Cumference

For a function $f$ whose antiderivative is $F$, I always interpreted $\int{f(x) \mathrm{d}x}$ as canceling out the denominator in the antiderivative: $=\int{\frac{\mathrm{d}F}{\mathrm{d}x} \mathrm{d}x}=\int{\mathrm{d}F}$, and then summing up the differentials to get $F$. So, the integral sign is an operator that acts on differentials.

alright if you understand thats great but whatever your writting down makes no sense to me good luck with it.

Sircumference has gone full retard but I have to defend him because we are hbar brothers

Daminark

@BalarkaSen ur face

11:06 PM

@0celo7 ...

I'm just trying to put together this fucking notation

What idiot invents notation that's illogical?

@SirCumference At the cost of rigor, this makes sense.

Q: If sequence of vector spaces is exact then the sequence of duals is also exact

0

Induced Exact Sequence of Dual Spaces I was able to prove the result for short exact sequences, but my instructor did not say short exact sequence, just sequence. So it is not given that the maps in the sequence are injective or surjective. Is there a counterexample to the sequence of duals bein...

Math is supposed to be the good subject, unlike physics

help!

I don't see what the fight is about

@Daminark no u

11:08 PM

@BalarkaSen The fight is about this question

32 mins ago, by Sir Cumference

Suppose we have a double integral $\iint{f(x) \;\mathrm{d}x \mathrm{d}y}$. Would it be correct to interpret this as: $\iint{\frac{\partial^2 f}{\partial x \partial y} \;\mathrm{d}x \mathrm{d}y}$, cancel out the denominator, and view it as summing:
$\iint{\partial^2 f}$?

Oh no, that's a bit problematic.

Also did you mean $f(x, y)$

like I said, Larky

@BalarkaSen Yeah, sorry

Ok, no it gets problematic once you involve two or more variables. The rigorous context of this whole story lies in differential forms.

Nah , you need a product measure

11:10 PM

@Zee No, he wants to view the 2-form $f dxdy$ as an exact form.

This has nothing much to do with measures.

It's not a definite integral, so to speak

See @LeakyNun

All right, I'm going to go and sulk

Hello. Hello. Lovely day, yes?

whats the deifnition of an exact vector space

@SirCumference I'd explain the story to you in more detail but I need to go to sleep and won't have time for 2 weeks to have an extended discussion. Here's a suggestion: Ask @TedShifrin about it, and he will explain this in greater detail and more clarity.

11:12 PM

Welp all right, I guess I'll head out

I'm off to bed for now.

@Faust well actually its the sequence of linear maps thats called exact

if the image of one is the kernel of the next

exactly equal, you might say.

the Integral is simply an operator with the dx specifying the range space

@HerrWarum can you have more than two steps then?

@Faust oh yes. even infinitely many

Exact sequence

An exact sequence is a concept in mathematics, especially in group theory, ring and module theory, homological algebra, as well as in differential geometry. An exact sequence is a sequence, either finite or infinite, of objects and morphisms between them such that the image of one morphism equals the kernel of the next. == Definition == In the context of group theory, a sequence G 0 → f 1 ...

DarkVampiric AbstractArtist

11:16 PM

wierd seems its outside of my level of understanding sorry ^^

are they applied to the range or to the whole space each time?

Find and solve the appropriate congruences.
Anklebiters Childcare Centre bought t toys. The toys came in packs of 10. The next day, at the start
of the day there were n children at the centre. The children were evenly divided into groups of 4, and
each group was given 6 toys. There were 2 toys left unused. Two toys were destroyed by the children’s
brutal style of play and had to be thrown out. Later on, m more children were dropped at the centre.
The children were then divided into groups of 6, with 7 toys per group. There were 6 (intact) toys not

@Faust I don't understand what you are trying to say. Yes each map is defined on the entire space each time just with the restriction that its kernel is the image of the previous one and its image is the kernel of the next one. Does that answer your question?

DarkVampiric AbstractArtist

m/6 *7 -10t =8. and n/4 * 6 -10t =2

m+n = 6x n=4y

@HerrWarum yes it makes sense thats why u cna have more than 2 :p

Yes, looks like you're the right track, and yes I'm working with mod 10.

you're on*

you cant find t ans a given number

you can only find t as some number plus a multiple of anthor number