Deven Ware

in set theory is the only time where they really distinguish between them

so it is a set. outside of set theory most people say class just to mean collection without worrying about anything

its contained in some amount of power sets of D

just the word

but the "class of all ordinals" is a proper class so we can't do much with it

for instance the ordinals are extremely useful

the objects inside the class may still be useful

well we just cannot use them like they are sets

@PeterTamaroff yes

for instance the class of all sets is a proper class

a proper class just means that it is a class i.e. is defined by a formula but cannot be a set

I added it as an edit, because it shows why I'm asking the first question, but essentially asks a second question about a different integral

would it be acceptable to post my important edit on this post math.stackexchange.com/questions/365152/… as a second question? or is it better left in this one

quick meta- question

The elements of the power set are by definition subsets of the original set

for the second part (a,b) = {{a}, {a,b}} and both a and b are in {a,b} so they are in the union set

(a,b) = {{a}, {a,b}} both {a}, {a,b} are in P({a,b}) and so {{a}, {a,b}} is in PP({a,b})

carried an extra one there somehow

woops sorry I meant 3/8

I'm unsure if I erred somewhere along the way though seems like an odd number

I ended up doing out the whole thing and getting \int^1_0 x^2 dF(x) = 7/16

is there a program which will calculate this numerically if i enter in "cantor function * x) integral

that seems like it should work, thanks for the help I'll do it out now and see

yeah I see

riemann-stieltjes integral

calculate \int^1_0 xF(x) dx where F(x) is the cantor function (devil's staircase)

it is essentially this

correct

this is 1/2

I don't see how tht would help me integrate

You see, even if I had that though

tbh I've never heard that term before, but I assume it means something like it's essentially the same in both intervals?

prove that it is "self-similar"?

(he wrote a where I write F)

he seem's to think (at least from his hint) that it can be done using properties of F ... rather than some sequence

yeah that's another of my concerns

I suppose not, however at the point of going down and figuring that out the solution seems to be getting a bit more convoluted than I would expect it to be

however thats likely unhelpful since we have u+2

I'm unsure you can get something like 1/18 \int^1_0 (u+2)f_n(u) du

but the ones on the edges seem to go to 0 unless I'm seeing it wrong, but that seems wrong to me, e.g it seems wrong that in 0,1/3 and 2/3,1 the integral would be 0

just take the limit as n\rightarrow \infty of the sum of these three values?

Okay Dylan sorry I'm quite slow at integration and concepts like this just getting to understand it, so we've got $\frac{1}{18}\int_0^1 uF_n(u) du for \int^{1/3}_0 F_{n+1} and we can do \int^{1}_{2/3} similarly, and $\int^{2/3}_{1/3} is always the 1/12 correct? but then I still can't see how to conclude

oh gotcha

@Dylan Sorry I think maybe i'm missing something silly how did you get to $F_n$ instead of $F_{n+1}$? "Write $u = 3x$ and work out the details; you get $\frac{1}{18}\int_0^1 uF_n(u) du$."

ok, I'm back sorry my friend needed something

See I knew it wouldn't be substantive enough for a question on the site ;)

should solve it, but then when I just define a function to be the solution to this and evaluate its derivative at 0 it doesn't give me 0, which was my initial condition

Essentially I'm just trying to get mathematica to solve the differential equation for a forced harmonic oscillator,

Hey guys I have a quick question about a differential equation in mathematica that I was hoping someone could help me with here, as its not really substantive enough to pose as a question on the main site