fallen lotus
OHHHH
#help-39
pearl pondBOT
pearl pondBOT
Available help channel!
heavy onyx
still a bit rusty on my mvc, im trying to understand what they did on both sides to get the result right above eq (4). im guessing there is some chain rule expansion involved but then idk how they got the RHS
pearl pondBOT
still a bit rusty on my mvc, im trying to understand what they did on both sides...
@heavy onyx Has your question been resolved?
cursive wraith
still a bit rusty on my mvc, im trying to understand what they did on both sides...
Differentiate U(lambda ...,...) = lambda U(...) with respect to lambda
The right hand side is lambda * constant (with respect to lambda)
So the derivative wrt lambda is that constant
Being U(S,V,...)
And then take lambda = 1 for the left hand side
heavy onyx
oh that makes sense
was confused with what they were differentiating wrt
thanks man!
.close
eager jewel
how to integrate (t^2+1)/(t^4+1)
pearl pondBOT
how to integrate (t^2+1)/(t^4+1)
toxic lichen
very painfully
eager jewel
ohk then how about
(cosec x +sin x)/(cosec x sec x + tan x sin^2 x)
that was original q..i simplified it by convering to sin and cos and then i took sin x = t
toxic lichen
ugh that looks even more ass
inland ivy
Just divide the numerator and denominator by t^2
And then think of a u-sub to simplify it
eager jewel
(1+1/t^2)/(t^2+1/t^2)
eager jewel
t-1/t?
inland ivy
Yes, and can you write the denominator in terms of it?
eager jewel
ye (t-1/t)^2 +2
inland ivy
Exactly
pearl pondBOT
pearl pondBOT
Available help channel!
night quail
What test / method would you go with to check and prove this converges / diverges?
cinder flower
comparison
sharp smelt
What test / method would you go with to check and prove this converges / diverge...
split it into two parts and then use boundedness of cos
ebon skiff
Omg its layla
cinder flower
splitting into two parts seems a little sus
cinder flower
Omg its layla
the one and only
ebon skiff
Are you actually the layla
cinder flower
the one and only
heavy onyx
try bounding it with a p-series
cinder flower
yep
ebon skiff
How s it going
cinder flower
it’s going okay other than no bf
cinder flower
you need bf too?
cinder flower
i know i was just trying to be funny
ebon skiff
Ah
Your humour is unmatched
As always
Well
Seeing as you re a girl
Do you have any tips
For me
pearl pondBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
ebon skiff
Sooory
heavy onyx
just tighten up your steps with proper notation
heavy onyx
the idea is fine
pearl pondBOT
cinder flower
what
cinder flower
i have no idea what you are saying
bronze heath
sup guys moveto dms
ebon skiff
In about 4 years
slow oak
@ebon skiff this is not appropriate for a help channel or in general
ebon skiff
The channel is closed but ok
slow oak
these channels aren't social channels either way
ebon skiff
Ok sorry boss
sharp smelt
these channels aren't social channels either way
even if they were...
pastel umbra
...this is rather disturbing behaviour
cinder flower
who tattled
pastel umbra
Bruh we can read the damn channel
slow oak
I am still back reading, ts is called triage while I take time to read
compact ridge
who tattled
👀
ebon skiff
Noooo
pastel umbra
That's like punching a man in front of a museum and then asking who called security
slow oak
skissue
night quail
im scared to ask for help again
night quail
caused chaos
cedar sentinel
im scared to ask for help again
you're fine
ebon skiff
I'm sorry gonk
slow oak
okay take a day off bleak posting
cinder flower
Bruh we can read the damn channel
the influx of people including a mod resonates helpers lounge share
rustic gate
indeed
cinder flower
i’m so smart
cinder flower
not denying it was shared in helper’s lounge i see
unborn abyss
_What didst thou expect_
.thank you for correcting that
rustic gate
.
cinder flower
hm is it helper’s lounge or helpers lounge
prime bramble
the latter
rustic gate
only your weird ’ could make it into the name of a discord channel
prime bramble
it should technically be the former though yeah
cinder flower
oh that would make a lot more sense
rustic gate
helpful lounge
pearl pondBOT
Available help channel!
midnight haven
A bag contains 5 white balls, 7 red balls and 3 black balls, if three balls are drawn one by one without replacement, find the probability that none is red
dusty jungle
yeah thats easier
dusty jungle
yeah
dusty jungle
yes
midnight haven
But ans is given as 8/65🥲
dusty jungle
hm
cinder flower
12/13 is way too close to 1
dusty jungle
P(all 3 red)= 7/15 x 6/14 x 5/13 right
these are dependent events
midnight haven
I can understand its not possible
dusty jungle
so you cant multiply them
cinder flower
not (none is red) means at least one is red
midnight haven
so you cant multiply them
Oh so what shud i do
dusty jungle
like the second probability being 6/14 depends on whether you took one red or not
midnight haven
not (none is red) means at least one is red
What
dusty jungle
So, shud i take
also yes this should be p(none red) = 1 - p(at least 1 red)
cinder flower
P(none red)= 1-p(all 3 red)?
this doesn’t make sense
why are you using the complement for this?
midnight haven
Oh ye
left frigate
pearl pondBOT
left frigate
how to tell this is not a bipartite graph
other than the fact that it is a complete graph
ancient slate
A complete graph with more than or equal to 3 points cannot be bipartite
autumn fossil
and it obviously cannot be partitioned into two sets of vertices s.t. there are no edges connecting vertices from same set. Because literally every pair of vertices is connected by an edge
autumn fossil
A complete graph with more than or equal to 3 points cannot be bipartite
we could strengthen this to more than 2 vertices actually
ancient slate
Oh yea
autumn fossil
only complete bipartite graphs are K1 and K2
tropic saddle
you can always just try to start partitioning the vertices
say we start at a
we put that in one of the two sets
then we need to put all neighbors of a into the other set
but then we already see that those have edges between them
so we are fucked
ancient slate
Also a bipartite graph with n points can have at most n^2/4 lines
left frigate
but then we already see that those have edges between them
i dont get this
suppose i put a in the first set
then i put all the others in the second set
what now
ancient slate
The second set cant have connecting lines between its points
tropic saddle
so b and c are in the second set
but b and c have an edge between them
thats not allowed in a bipartite graph
ancient slate
Yea
tropic saddle
so we are done
left frigate
so vertices in the same set must not be connected with each other?
tropic saddle
yes
left frigate
and if it is complete bipartite
then every node of first set should map with every nod of second set?
tropic saddle
yes
pearl pondBOT
pearl pondBOT
Available help channel!
ancient slate
I forgot which kind of integration include the integrating factor I
ancient slate
Does anyone know?
restive garnet
iirc you need that for solving differential equations
hard matrix
pearl pondBOT
toxic lichen
ok so $\frac{y}{x-z} = \frac{y+x}{z} = \frac{x}{y}$
jolly parrotBOT
Ann
hard matrix
yea
toxic lichen
most obvious beginning seems to be to let all this = k and try to express other stuff in terms of k
hard matrix
Any particular known standard approach
toxic lichen
don't know of anything else sophisticated
hard matrix
most obvious beginning seems to be to let all this = k and try to express other ...
Lol , I tried and failed miserably
toxic lichen
maybe some of that "componendo dividendo" bullshit but i do not see how to apply it here productively
toxic lichen
well another way would be to attempt to put one of the letters = 1 and try to solve for the others
a bit cheaty but it works ig
hard matrix
well another way would be to attempt to put one of the letters = 1 and try to so...
Hmmm now how does that work
toxic lichen
basically if you put z = 1 then you will be finding x and y and the ratio will be x : y : 1
this assumes z is not 0
hard matrix
well ig that would be easier
lol u might be on to smth
I have found some usefu reults using ur trick
I got 2:4:3
hard matrix
well in ma book answer is given
x/4=y/2=z/3
I got smth similar so maybe I messed up some proess
can u check these
@toxic lichen
hard matrix
Oh :(
toxic lichen
or wait
well you screwed up somewhere but i cbf to unrotate the pictures and find where
hard matrix
cbf?
toxic lichen
can't be fucked
solid drum
Hello, I would like to know how are people coming up with reductions from 3 SAT to Independent Set
Like the way the proof is constructed I would have never guessed it
plush bramble
Show the proof you're reading
plush bramble
Just seems like a case of people spending a long time solving open problems and refined over time.
solid drum
So I believe I will get a more "clear" reduction on my exam?
Since our instructor even does not understand how they did the proof
plush bramble
No idea I'm not your instructor
solid drum
pearl pondBOT
Available help channel!
sleek sandal
so
sleek sandal
we can only construct the inverse if A, B, and C are invertible matrices?
sharp vigil
i don't think we'd have much guarantee of invertibility otherwise
sleek sandal
ok
vital estuary
you might be able to get away with B not being invertible
fast canyon
thanks they're probably gonna ask a cheeky quesiton on that
piano concerto
sleek sandal
don't tell me u know classical
fast canyon
don't tell me u know classical
i dont. i do know yuja wang tho
pearl pondBOT
pearl pondBOT
Available help channel!
spring gale
Why is it that Dirac-delta function, which is:
[
\delta(t - t_0) = \lim_{\epsilon \to 0} \delta_{\epsilon}(t - t_0)
]
shows that
[
\int_{0}^{\infty} \delta(t - t_0), dt = 1?
]
Is that not weird?
jolly parrotBOT
e8
sharp vigil
why not? each of the delta_epsilon's has that property
spring gale
right, but if you graph it
you will see at t_0, it's infinity
With no thickness
Also would this not be even weirder because laplace of that function is 1, so is it not a property that lim s-> infinity F(s) = 0. Why is the laplace of this 1, because if you take the limit of 's' to infinity, it's still 1, and that contridicts that first property of functions in s-space which have been laplaced!
tropic saddle
the dirac delta function is not actually a function in the usual sense
there are ways to make precise what it actually is but presumably those arent relevant in your course
spring gale
the dirac delta function is not actually a function in the usual sense
What do you mean?
tropic saddle
well there is no function in the usual sense which satisfies f(x)=0 everywhere except x=0 and int f(x) dx=1
spring gale
That's not really a satisfying answer for my inital question
tropic saddle
the way I interpreted your original question is that the delta function seems weird. frankly the answer is that it is weird because its not even really a function
its just something to get used to
unless you want to invest a few weeks into understanding what it actually is
wind lagoon
Consider the $\sigma$-field $\sigma(X)\lor\mathcal{B}$ (the smallest containing $\sigma(X)\cup\mathcal{B}$), where $X$ is any random variable and $\mathcal{B}$ some $\sigma$-field. Is it true a nonnegative $\sigma(X)\lor\mathcal{B}$-measurable function can be written as $h(X)Z$ for some nonnegative $h$ and $Z$, where $Z$ is $\mathcal{B}$-measurable?\
I know if a function is $\sigma(X)$ measurable, we can write it as a function of $X$, so say $h(X)$. But I don't understand why a nonnegative $\sigma(X)\lor\mathcal{B}$-measurable function could be written as a product like that.
jolly parrotBOT
psie
barren path
wind lagoon
or even to indicator functions
Hmm, ok. Suppose we look at $\mathbf{1}_A$ where $A$ is $\sigma(X)\lor \mathcal{B}$-measurable. How is this set characterized? Can we write it in some special way, e.g. intersection of sets in $\sigma(X)$ and $\mathcal{B}$, respectively?
jolly parrotBOT
psie
tropic saddle
I dont know. just trying to give ideas
pearl pondBOT
@wind lagoon Has your question been resolved?
pearl pondBOT
@wind lagoon Has your question been resolved?
wind lagoon
.close
pearl pondBOT
ivory basin
Predicates look correct
Premises look correct
Conclusion looks correct as well
It is valid, however there is a hidden step in the middle
Which is the introduction(?) rule for OR
Aka P → P ∨ Q
Wait no what am I saying
Yup that's correct now
pearl pondBOT
@charred kindle Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
daring bay
Due to an invention in the food industry that created a new flavor enhancer
has developed with gummy bears, we now want to test whether the proportion of children who
Gummy bears may have increased from the previous 70% (counter-hypothesis). For this purpose, 200
Children tested.
a) Specify the test size.
b) State the null and counter hypotheses and determine the
largest possible rejection range at a significance level of 2%.
Furthermore, decide and justify whether the null hypothesis is rejected,
if 151 children like the new gummy bears
daring bay
can someone explain what my teacher did in b)
why c + 1
oh because its increased
but i dont understand the p(x .... part
sly garden
[0, c] and [c+1, 200] covers the entire discrete sample
daring bay
uhh
sly garden
significance level of 2% means p<0.02 to reject the null hypothesis H_0
sly garden
the x is the number of kids who liked the new gummy bears
daring bay
oh so p(x>= c+1) is the general thing for alpha mistake?
sly garden
-# forgot what an alpha mistake was
but in general you're looking for the lowest number C such that P(x≤c) = 0.02
daring bay
the type I error
sly garden
copy
sly garden
actually correction
daring bay
so basically your looking for the first number thats bigger or equal to c
sly garden
no hang on
ur good i confused myself, disregard
daring bay
you can calculate bernoulli distributions, yeah?
yes
but i dont understand
why are we looking for c
c is basically x right
sly garden
we're trying to figure out if P(x≤151) is less than 0.02
sly garden
wait on (b)?
daring bay
State the null and counter hypotheses and determine the
largest possible rejection range at a significance level of 2%.
wait bro @sly garden where did the 1- come from
the fuck
sly garden
P(x≥c+1) and P(x≤c) add to one
your professor has it wrong though because we can't reject the null H0 at 151 successes out of 200
sly garden
yes, apologies. i'm still not sure what "the largest rejection range" means tho
daring bay
`P(x≥c+1)` and `P(x≤c)` add to one
oh yeah but
the 1 in the bracket where did that go
sly garden
my guess is that it would have to be the largest range that we could reject a hypothesis at [0, c] or [c+1, 200] but i have NO idae
sly garden
the 1 in the bracket where did that go
since $P(x \geq c+1) + P(x \leq c) = 1, 1-P(x \leq c) = P(x \geq c+1)$ by basic algebra
jolly parrotBOT
Mirror
daring bay
but the c+1 inside the bracket yk they just dissapeared
but its alright
ill just memorize that
sly garden
you're thinking of the internal inequality as a variable and you should not be
it's two cases: either x≤c OR x≥c+1
sly garden
👍
sly garden
right because it's wrong
daring bay
how did the sign flip
sly garden
the sign should flip because they subtracted one and multiplied by -1
but the probability calculations in (c) are just wrong
daring bay
yes ik but
multiplied by -1
why
did he do that
OH WAIT
i see it
my bad
om gis ee it
sly garden
because otherwise the equation would be $-P(x \leq c) = -0.98$
daring bay
its from -p
jolly parrotBOT
Mirror
sly garden
which while true is not helpful
daring bay
sometimes m yhead doesnt work
sly garden
allg
pearl pondBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
so
theres a function
in the calculator that lets u see the list of the kumulated chance
but im kind of confused on how to calculate this
sly garden
you're looking for P(x≤151) GIVEN that p=0.7
if that number is less than 0.02, you can reject the null H0
daring bay
you're looking for P(x≤151) GIVEN that p=0.7
i dont understand
daring bay
what does that give you?
so i can use a list thing
i can enter my n, 200
and my p 0,7
but then i can enter numbers for k
sly garden
right, okay. what does entering 151 yield?
sly garden
151 for k
daring bay
yes
but heres the problem
we dont know before hand
that its 151
so how do we end up entering that
sly garden
we can use 151 to check the null hypothesis
let's do that first
i get this
since P(X≤151) < 0.98, i cannot reject the null hypothesis
sly garden
right
daring bay
okay but
like
how do we end up with 151
it was 153 btw
the k
oh
wait
ur using the 151 from the already given
sly garden
yes
sly garden
then you don't have a hypothesis to test
daring bay
wtf
man i wish my head would work like yours
i truly just wish i wasnt a stupid piece of sjit
sly garden
i truly just wish i wasnt a stupid piece of sjit
knock it off, be nice, you're learning
can you talk to the prof?
sly garden
so here's the situation
daring bay
im gonna keep doing these exercises
its a 45 minute test about bernoulli and hypothesis
sly garden
at 153 do you see how P(X≥153) is 2.49% > 2%?
but at 154 it's 1.69% < 2%?
i misspoke, and i'm sorry. you're looking for the lowest value X such that P(k<X) is less than your significance value (which is the jump from 153 to 154)
sly garden
because it's the lowest number where you can't reject the null hypothesis
remember c is set up such that any value in [0, c] means we can't reject H0
at 154 we can, at 153 we can't
sly garden
what about it?
daring bay
but for x<= 153
the chance is 98,38%
OHH
so its the first value that comes after 98%
sly garden
yep
daring bay
the x=<c really confuses me
x is basically c right
thyre both just different variables for the kids who like gummy beats
sly garden
this is why i don’t like that the prof used c
sly garden
basically
sly garden
ye basically
daring bay
but at 154 it's 1.69% < 2%?
wait so i dont understand why the h0 is denied when significance is lower than 2%
sly garden
basically: there's less than a 2% chance of a sample actually showing those results if the hypothesis were true
daring bay
basically: there's less than a 2% chance of a sample actually showing those resu...
oh
im just overthinking it
significance is that u think that h0 is wrong even though its correct
yeah i dont understand i swear i just dont understand
yeah i overthinked it
so you still accept the h0 @sly garden
pearl pondBOT
@daring bay Has your question been resolved?
daring bay
@sly garden yo bro for the c)
Determine probability of type I error if the critical number (3)
c =149
i dont understand
why can you just calculate it like this now
i mean like
p(x>=150) is the significance?
sly garden
why can you just calculate it like this now
you absolutely can
daring bay
bro i dont understand please
what does the 0,93 even mean
it means the chance that 149 kids like gumym bears right
sly garden
but at 154 it's 1.69% < 2%?
149 or fewer
daring bay
okay so
1-0,93 is the significance
but it doesnt make sense
how
significance lkke how
what does it even mean
pearl pondBOT
@daring bay Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
shut flicker
Alice tosses 3 coins; Bob tosses 2 coins. Alice wins if she has more heads than Bob. If it is a tie, then they flip one more coin to decide the winner. Find the probability that Alice wins. i think ive done it wrong, since im pretty sure probability alice wins should be higher than 1/2
toxic lichen
what about if bob tosses 0 heads
sleek grotto
ъ
toxic lichen
for that matter what if they both toss 0 heads and Alice wins the tie break
pearl pondBOT
pearl pondBOT
Available help channel!
shut flicker
There is a 0.5 probability that it will rain on a given day. What is the probability that during a week there will be consecutive rainy days? i did this with stars and bars method, (considering 1-P(no consecutive rainy days)) and got 94/128, i feel like this could be done with recursion, not 100% how tho
toxic lichen
sure. let p_n denote the probability that it does not rain on any consecutive days in a timespan of n
then considering the last two days of such a timespan, we have that the condition of "no consecutive rainy days" is satisfied in exactly the following scenarios:
- day n is sunny, and the first n-1 days meet the condition
- day n is rainy, day n-1 is sunny, and the first n-2 days meet the condition
hence $p_n = \frac12p_{n-1} + \frac14p_{n-2}$
jolly parrotBOT
Ann
shut flicker
thanks makes plenty of sense, i suppose i will still need to find p_n for like 2 and 3 and work up
coldddd i got the same answer
.close
pearl pondBOT
pearl pondBOT
Available help channel!
rare holly
hello why is this step wrong
pearl pondBOT
hello why is this step wrong
prisma kernel
where did the 28 come from?
summer anchor
hello why is this step wrong
multiplying by 2 on both side should remove the 2 on the denominator on the left
What you just did is like multiplying by 4 on the left and 2 on the right
rare holly
where did the 28 come from?
i multiplied everything by2
prisma kernel
Read what Mec sent
blissful cloak
when you "multiply everything by 2" that means all the terms on either side
(x+12)/2 times 14 is one term
not two different ones
so the effect is multiplying by an extra factor of two on the left-hadn side
rare holly
so the effect is multiplying by an extra factor of two on the left-hadn side
i see
how can you tell if its the same factor or a diffrent factor?
blissful cloak
factors are separated by addition and joined together by mutliplication
rare holly
addition meaning 2 diffrent factors?
prisma kernel
Yeah it would have worked if it was $\frac{x + 12}{2}$ + 14
rare holly
multiplication meaning same factor?
jolly parrotBOT
doctorstrangejr
blissful cloak
2+3 are two different terms, 2x3 is one
rare holly
factors are separated by addition and joined together by mutliplication
wow nice explnation thanks
i had this mis conception
thank you
.close
pearl pondBOT
pearl pondBOT
Available help channel!
quick venture
pearl pondBOT
quick venture
can someone explain how they removed the minus sign from the half
sly garden
for all integrals, $\int_{a}^{b}f(x),dx$ = $-\int_{b}^{a}f(x),dx$
jolly parrotBOT
Mirror
pearl pondBOT
@quick venture Has your question been resolved?
quick venture
ah okay ty
quick venture
pearl pondBOT
quick venture
can someone explain what happens after the step with the ?
is the integral of du=u
opal cairn
Yeah the integral of 1 is u
pearl pondBOT
pearl pondBOT
Available help channel!
modest tulip
need to turn into ode?
pearl pondBOT
need to turn into ode?
modest tulip
but im not sure what this is
advection-diffusion equation
i need to determine " How does angular mixing speed affect the time required to achieve a uniform concentration of chocolate powder in milk?'
opal cairn
not sure if i can help but is D a constant?
if yes then maybe you could solve it by separation of variables
pearl pondBOT
@modest tulip Has your question been resolved?
opal cairn
yeah sure
pearl pondBOT
pearl pondBOT
Available help channel!
steady wolf
hi i just wanna know if chat is correct, chat says only the highlighted option is wrong? but i thought the ones with the linear combinations are also not a basis like specifically the second and third span
cinder flower
what does “wrong” mean here
i don’t think the highlighted one should be ticked
i would tick 3 and 5 only
minor tapir
what does “wrong” mean here
I meant right oops
cinder flower
what is your reasoning for 2?
minor tapir
because
we have a linear combination of b2 and b3
Wait is it because
B2 is not in the set
So it works?
minor tapir
i would tick 3 and 5 only
Okay I agree
Can yiu help me with this quesiton too pls
I swear no one helps with linear algebra now:(
cinder flower
:(
minor tapir
cinder flower
i need to go eat my food
pearl pondBOT
@steady wolf Has your question been resolved?
prime bramble
Can someone help me
a rotation matrix (that doesn't rotate by any multiple of 2pi) has no (real) eigenvalues (nothing gets stretched or squished, only rotated), so its characteristic polynomial should have no (real) roots
also, since the matrix is a map from R^2 to R^2, the characteristic polynomial must have a degree of 2
prime bramble
you can write (0, 1, 1)^T as e_2 + e_3 and use the linearity of T to deduce what T(e_3) is
spoiler: ||your answer is right||
outer hare
Im having throuble understanding this notation. Why are elements in R^k sequences?
prime bramble
Im having throuble understanding this notation. Why are elements in R^k sequence...
the elements of R^k aren't sequences
they're k-tuples
the lemma is considering a sequence of k-tuples
x^(n) is the nth element of the sequence in the same way x_n is the nth element of a sequence of real numbers (x_n)
outer hare
What does it mean when it says $x_j^{(n)}$ converges then?
jolly parrotBOT
BOSS
prime bramble
it means that the jth component of the sequence x^(n) converges
outer hare
which is a sequence?
prime bramble
the sequence looks like $(x_1^{(1)}, x_2^{(1)}, \dots, x_k^{(1)}), (x_1^{(2)}, x_2^{(2)}, \dots, x_k^{(2)}), \dots$
outer hare
I made the same mistake lmao
prime bramble
dang it 
prime bramble
which is a sequence?
mhm, look at the first component for instance
outer hare
ok
jolly parrotBOT
higher!
outer hare
Ok wait so lets say
prime bramble
by considering each component
and the lemma says that the sequence of k-tuples converges iff each of the k component sequences converges
outer hare
I define $\mathbb{R}^2 = {(x,y) \mid x,y \in \mathbb{R}}$
versed mica
you have a sequence of vectors and then you consider the sequence in R given by the jth coordinate in each of those vectors in your sequence
jolly parrotBOT
BOSS
outer hare
you have a sequence of vectors and then you consider the sequence in R given by ...
ok so
x would just be R
or lke any of those elements would just be R
or the sequence that constructs R
versed mica
for the sequence of vectors to converge to some vector they're saying it needs to converge coordinate wise
outer hare
Ok so for the notation lets say i define my sequence as X = (1,2),(3,4),(5,6)...
Then $x^{(n)}_1$ is just 1,3,5.....
versed mica
**BOSS**
here its like having a sequence of pairs (x_1, y_1), (x_2, y_2), ..., (x_n, y_n) and saying that both the sequence x_1, x_2, ..., x_n and the sequence y_1, y_2, ..., y_n converge to some limits in R
jolly parrotBOT
BOSS
prime bramble
sure, then the sequences the lemma is talking about are {1, 3, 5, ...} and {2, 4, 6, ...}
outer hare
ok cool
ngl that was some confusing notation lol
so each elemet is just the sequence of elements in that coordinate
prime bramble
they had to double up on the indices because there's a coordinate index and a sequence index
outer hare
Yeah I read the note I just feel like one sentence on what it is could be better
outer hare
you have a sequence of vectors and then you consider the sequence in R given by ...
smth like this
ty tho my tired brain appreciates the explanation
Oh and the lemma is just saying each indivisual coordinate also has to converge for the entire tuple to
that makes sense
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pearl pondBOT
outer hare
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pearl pondBOT
✅ Original question: #help-39 message
outer hare
back to the notation thin if ur still here @versed mica
@prime bramble
Is there anything specifying every combination exists/
prime bramble
what do you mean?
outer hare
like for example if you look at this proof
Its just saying we replace every coordinate with its convergent subsequence
what guarantees that a combination of those exists
like in my example of X = (1,2),(3,4),(5,6).
(1,4) isnt in there
if that makes sence
so it cant be part of a subsequence
prime bramble
what guarantees that a combination of those exists
...B-W in one dimension? 
I'm not exactly sure what the concern is 
outer hare
Like, for a tuple order matters right
prime bramble
since x^(n) is bounded, each coordinate sequence is bounded, so you can use B-W on each component
outer hare
Yes, but if you look at the proof it does it individually for each sub sequence right
prime bramble
yeah, sure
prime bramble
you've got it backwards
outer hare
X = (1,2),(3,4),(5,6).... wont have (1,4)
even though the coordinates do have those elements seperately
prime bramble
we start with (x^n), a bounded sequence in R^k
outer hare
ok
prime bramble
we are not constructing x^(n)
the proof uses bad notation imo
they shouldn't have called the final subsequence the same thing
should've called it y^(n) or smth
outer hare
im still confused lmao
ok just to make sure
for this example X = (1,2),(3,4),(5,6)....
A sub sequence would not be (1,4), (3,8)....
even through if we pick and choose for each coordinate sequence they do have those elements
prime bramble
no, elements of a subsequence must be elements of the sequence
(1, 4) isn't in the sequence
outer hare
ok good
hmm
what is the proof doing then
Oh is it like
building on the last one
its doing x_1 first
which is why it works/
?
prime bramble
it's starting with a bounded sequence of vectors and then zoning in on each component sequence
then it's applying B-W to each component sequence to get a convergent component subsequence
then attaching all those subsequences together into a vector sequence
outer hare
ok so its just doing them one by one so that the points exist
not speratly and putting them all together
that makes sense lmao
prime bramble
what do you mean one by one?
prime bramble
it's most certainly doing all of them at once, it's just not saying it that way
outer hare
then after those remaining elements its doing x_2
prime bramble
whether you do them all at once or one at a time isn't really relevant here anyhow
the point is that we can do it to all of the components
outer hare
whether you do them all at once or one at a time isn't really relevant here anyh...
If u do them all at once
You would get combinations that dont match
prime bramble
why not?
outer hare
ok so what I thought was going on was they took every coordinate sequence
prime bramble
you aren't picking a sequence of vectors
outer hare
then took its convergent subsequence
prime bramble
you're looking at all the components at once
outer hare
and replaced it
prime bramble
and picking a convergent subsequence of each component
ah, I think I see the confusion 
I didn't read their proof closely enough
outer hare
Yeah i just read the proof wildly incorrectly lmao
Im trying to see what allows us to gaurentee enough elements for the second coordinate to converge after removing all the vectors while changing the first
prime bramble
the author's going component by component, first throwing out vectors in the sequence until x_1^(n) converges, then throwing out vectors in the new sequence till x_2^(n) converges, etc
in the end, the sequence of vectors converges
prime bramble
what I thought they did was: consider each component separately, replace each component with a convergent component subsequence, and then attach those all together
outer hare
nvm i was thinking of some abstract example but that would not converge even for the toople
outer hare
what I *thought* they did was: consider each component separately, replace each ...
see this is what i thought would not work
prime bramble
tsk tsk, I need to work on my reading comprehension 
outer hare
because then you get combinations that are not in the original sequence right
like the (1,4) example
prime bramble
oh huh, I just realized what you were getting at, and you're right
that's totally my bad, I'm not sure what I was thinking
prime bramble
whoops, I guess I need to work on my thinking too 
prime bramble
thank you for correcting my silly mistake, I appreciate it c:
hopefully I didn't end up instilling some misconceptions 
outer hare
no your ok this was helpful lmao
Ok wait
I do have like
something im lost by then
in the same proof, what if they are bounded but never line up
like suppose one is osolating from 0-5, and another is osilating from 6-7 (real numbers), but they reach their peaks at different times
so then when we throw away the coordinates from the first bounded sequence,
oh
monotonic
nvm
ok well
that answers it lmao
prime bramble
prime bramble
outer hare
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pearl pondBOT
prime bramble
have a good night yourself c:
pearl pondBOT
Available help channel!
sharp galleon
pearl pondBOT
iron basin
sharp galleon
Lol
cinder flower
she can select the 5 usd dollar coin then a 2 usd dollar coin
or in the other order
cinder flower
so it's like 1/5 * 2/4 + 1/5 * 2/4
cinder flower
those are all the usd dollar amounts that can be made with two coins
sharp galleon
those are all the usd dollar amounts that can be made with two coins
yeah yeah
I forgot
the 1$ coin lol
thanks
.close
pearl pondBOT
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Available help channel!
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dusk willow
you can probably use the CLT here (by the word "approximation" I think they intend for you to use it)
bitter herald
The distribution in the question itself is a binomial distribution
bitter herald
ms said mean was 110*.25
The mean of a binomial distribution is np which is this
You should approximate the binomial distribution to a normal distribution
Which is generally valid if np > 5
So basically you need to appeoximate $X\sim B(110, 0.25)$ with a normal random variable $Y \sim N(\mu, \sigma^2)$
jolly parrotBOT
pearl pondBOT
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Available help channel!
iron dust
Is it possible to simplify this
pearl pondBOT
Is it possible to simplify this
ivory basin
Yes
rotund ferry
It’s (9a^-4b^6)/(a^8b^-2)
$$\frac{a^m}{a^n} = a^{m-n}$$
jolly parrotBOT
Matcha
iron dust
If I divide 9a^-4 with a^8 then I need to divide b^6 and a^8 too which is impossible
warped violet
I swear I saw this exact question yesterday
warped violet
If I divide 9a^-4 with a^8 then I need to divide b^6 and a^8 too which is imposs...
All you have is multiplication
If it's easier you can just split the fraction
iron dust
How
warped violet
$\frac{x \cdot y}{m} = x \cdot \frac{y}{m}$
jolly parrotBOT
USS-Enterprise
warped violet
Or rather
$\frac{x \cdot y \cdot z}{m \cdot n} = x \cdot \frac{y}{m} \cdot \frac{z}{n}$
jolly parrotBOT
USS-Enterprise
rotund ferry
If I divide 9a^-4 with a^8 then I need to divide b^6 and a^8 too which is imposs...
That's not how things work
iron dust
So it’s 9a^4 + b^4
warped violet
Where did I ever type a plus?
iron dust
Cause it is?
warped violet
Is it possible to simplify this
iron dust
So it’s 9a^4 + b^4
So this but with multiplication
iron dust
9a^-4/a^8 * b^6/b^-2
warped violet
Yes
warped violet
**Matcha**
Now use this
jolly parrotBOT
Xavier 🌺
.exp rules
ivory basin
#1071226369071136979 for your perusal
warped violet
<#1071226369071136979> for your perusal
Yeah I know. I am a lazy individual though
ivory basin
Lmao fair
warped violet
Yes
iron dust
Answer say it’s
golden valve
If I divide 9a^-4 with a^8 then I need to divide b^6 and a^8 too which is imposs...
u dont have to divide b by a
if you have 3*4/2
do you divide both 3 and 4 by 2
or js 4?(3 if you are a psychopath)
iron dust
Idk
golden valve
js divide a by a and b by b
iron dust
I did
golden valve
The original question was this
so a^(-2-4)
iron dust
9a^-4 : a^8
golden valve
The original question was this
b^3+1
iron dust
You don’t understand it
golden valve
9a^-4 : a^8
:?
iron dust
What the heck are you talking about
golden valve
How does this work?
minus power can be made positive
to do that
take the term in denominator
i should reverse its position from up to down
or down to up if needed
iron dust
So it’a
1/9a^12?
iron dust
Fucking why
verbal whale
You don’t understand it
Maybe because what you've done is wrong or even nonsense, you know?
jolly parrotBOT
Alberto Z.
verbal whale
$$A^{-1}=\frac{1}{A}$$
golden valve
$$A=\frac{1}{A^{-1}}$$
jolly parrotBOT
fysch
golden valve
this is also true
golden valve
**fysch**
wherever the powers are negative switch the position from down to up (here) or up to down
iron dust
,w ^4sqrt(9x^3y-2)
jolly parrotBOT
pearl pondBOT
@iron dust Has your question been resolved?
iron dust
Cornballs
bronze heath
?
warped violet
midnight haven
udo
midnight haven
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dusk willow
!done
pearl pondBOT
If you are done with this channel, please mark your problem as solved by typing .close
dusk willow
it's .close
latent quail
.solved
shut flicker
I have two identical packs of cards. I take each pack and shuffle it separately, placing them both face down in the table. I then proceed to play a game of snap with myself (being a mathematician I have no friends). I compare the top card from each pile, and then compare the second card from each pile, and so on. What is the probability that I continue in this way all the way down the piles, and never find an exact match in the 52 pairs of cards? hi can someone show the probabilistic and combinatorial way of doing this?
hot timber
Uh
shut flicker
i was thinking abt fixing one pack of cards, and then working out the the probability that the second deck perfectly doesnt match the first, but im not entirely sure abt this
hot timber
so when you take the third card you discard the first card?
do it work like that?
ohh
ok I understand
shut flicker
like we have two decks side by side and we take the top from each and hope they match i think yh
hot timber
what’s an exact match, both the designation and the sign?
shut flicker
yeah so 7 of hearts and 7 of hearts