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8:05 AM
@TheSimpliFire I need help to prove a set theory question
To prove $(A-B)-C=(A-C)-(B-C)$
My attempt
$(A-B)-C=(A \cap B') \cap C'$
$=(A\cap C') \cap (B' \cap C')$
$=(A-C)-(B'\cap C')'$
$(A-C)-(B \cup C)$
But $(B-C)\ne (B\cup C)$
So where am I going wrong?
@TheSimpliFire
 
back
@Mathphile ?
The intersection operation is associative, not distributive
 
FACEPALM
Figured it out
 
 
3 hours later…
10:55 AM
1
Q: Next primes of the form $n^n - (n-1)^{n-1} - (n-2)^{n-2} - (n-3)^{n-3} - ...- 3^3 - 2^2 - 1^1 - 0^0$

Dimash KLet $Q(1) = 1^1 - 0^0$ $Q(2) = 2^2 - 1^1 - 0^0$ $Q(3) = 3^3 - 2^2 - 1^1 - 0^0$ $Q(4) = 4^4 - 3^3 - 2^2 - 1^1 - 0^0$ and so on... Here I take $0^0 = 1$ . I found that $Q(2)$, $Q(4)$ , and $Q(7)$ are prime , but after that I didn't find anymore primes up to $Q(1000)$. I found these some regular p...

Can anyone doublechecke the range upto $n=6\ 800$ ?
 
11:46 AM
Can anyone doublechecke the range upto $n=7\ 600$ ?
 
 
8 hours later…
7:43 PM
i have come back to post a clock
Also, we should consider having a simplifire discord I would be more active, I've just drifted away from SE due to incidents and such
 
 
1 hour later…
9:12 PM
@Quintec Sure, I can invite all of you to a server if you want (what's your discord username?). I also hope you're doing ok
I like the clock
 
@TheSimpliFire would a question of creating your own discontinuous notion of distance regarded as recreational math and fit for the room?
 
@MoreAnonymous Post whatever you want
 
As long as your cool with it :)
1
Q: Distance and Covariant derivative with a strange metric?

More AnonymousBackground Here's something I was wondering about. Let the line element between $2$ infinitesimally close points be given by: $$ ds^2 = (a_s)^2 g^{\mu \nu} dx_\mu dx_\nu$$ Where $a_s$ is an arbitrary number at each point $s$. Due to the factor of $a_s$ this is obviously discontinuous. Using this ...

 
What's $g^{\mu\nu}$? I can't imagine a situation where that expression would be preferred
And I've never seen the derivative operator being rooted
 
@TheSimpliFire it;'s the metric
 
9:25 PM
OK, I gtg
Talk later
 
Alright
@TheSimpliFire It's quite common in general relativity and differential geometry for example:
3
Q: Distance between two points on a surface with metric $g_{mn}$

Beta DecaySay you have a two dimensional surface with a metric tensor $g_{mn}$ on which there are two points with coordinates $(\theta_1, \phi_1)$ and $(\theta_2,\phi_2)$, how would you calculate the distance between these points? My initial idea would be to solve the geodesic equation: $$\frac{d^2 x^a}{...

 

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