what is it
#help-38
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boreal shuttle
it doesnt seem like an easy equation to solve 
you sure of the expression ?
@woven sigil its 9x^2 or 2x^2 ?
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steep knot
what is it
|| 5/(3x+2)² + 4/(3x+2)(3x-2) - 1/(3x-2) = 0
5(3x-2) + 4(3x+2) - (3x+2)² = 0
15x - 10 + 12x + 8 - (9x²+12x+4) = 0
27x - 2 - 9x² - 12x - 4 = 0
9x² - 15x + 6 = 0
3x² - 5x + 2 = 0
(3x - 2)(x - 1) = 0
x = ⅔, x = 1 ||
boreal shuttle
|| 5/(3x+2)² + 4/(3x+2)(3x-2) - 1/(3x-2) = 0
5(3x-2) + 4(3x+2) - (3x+2)² = 0
15x...
bro i couldnt read what he wrote
steep knot
bro i couldnt read what he wrote
wdym
boreal shuttle
thats how i read it lol
while it was 12x instead of 2x , and 9x^2 instead of 2x^2
your method is good tho
steep knot
your method is good tho
thanks
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blissful prawn
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blissful prawn
Hi, how do I answer this Q? What is easiest way to answer this Q, and Q's similar to this one?
In math discussion, they said I can use fractions I think?
But im not sure how.
So far how many marks would I get for this Q?
/3
foggy nymph
In math discussion, they said I can use fractions I think?
Yeah that’d be the easiest way imo
How would you rewrite 1.2 as a fraction?
blissful prawn
1.2 / 10?
foggy nymph
Ex: if you have 20.22, you just count how many times you “move” the comma and use that as your zeros: 20.22 = 2022/100
blissful prawn
What do I do then?
foggy nymph
yup
foggy nymph
you tell me, how many times did you move the comma
foggy nymph
exactly
foggy nymph
you gotta divide them, right?
foggy nymph
do you remember how to divide fractions?
foggy nymph
remember that it’s 74.88 / 1.2 NOT 1.2 / 74.88
also, are you sure that 7488 * 10 = 74.888 ?
blissful prawn
No
Good ?
7488/100 x 10/12
Good ?
Which is
74880
/100
Ooops
Over
1200
foggy nymph
you can keep going, notice that 7488 is an even number, and 120 also is
blissful prawn
7488/60
7488/10
7488/2
So it is 7488/2
?
Am I right ?
And how do I work that out
7488/2
?
blissful prawn
Yes
foggy nymph
“Removing” the zeros only works when you’ve got zeros in the denominator and the numerator
but, do you see a zero in 7488?
blissful prawn
No
foggy nymph
but you know that both of them can be divided by two as they’re both even, right?
in other words
blissful prawn
Yes
foggy nymph
you haven’t done anything to 7488
foggy nymph
no
when you reached 936/15, you were doing good
but your denominator has to be an integer
(and your numerator too)
blissful prawn
I'm saying how do u know mathematics?
foggy nymph
I’m a mathematics student at college xd
blissful prawn
Do u know calculus?
foggy nymph
yeah?
blissful prawn
complex numbers?
foggy nymph
936/15 = 312/5 as both of them can be divided by 3
5 is a prime number, and 312 cannot be divided by 5. Therefore you can’t keep going. You do 312/5 by hand which is way easier and you get 62.4
That’s your answer
foggy nymph
no
you can’t do something on your numerator ignoring your denominator
that’s a mistake
blissful prawn
what is algebraic topology
?
No
What is it?
I know topology is summed up by one theorem.
Do u know what theorem that could be?
Do u know what theorem it could be?
blissful prawn
Do u know what theorem that could be?
For this
It is summed up By this theorem
The theorem is called
Four color theorem
gray rock
Four color theorem
I'm not even gonna elaborate but n o
gray rock
yes, and it comes up in graph theory
and you can't exactly sum up topology in a single theorem cause it's an entire field, it's like saying you can sum up number theory in a single theorem
you can't, it's just too vast
foggy nymph
and you can't exactly sum up topology in a single theorem cause it's an entire f...
me and peano against the world
blissful prawn
and you can't exactly sum up topology in a single theorem cause it's an entire f...
It is summed up By one theorem.
Topology is anyway
And that theorem is
Four color theorem
This is what im sayint.
Saying
gray rock
gotcha
blissful prawn
Am I right?
gray rock
No
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broken cave
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broken cave
Okay so y=max{x,1}
So y={(1,1),(2,1),(3,1)} like that ?
broken cave
if x>=1 then x otherwise 1
Am I right or missing something
lilac flame
Okay so y=max{x,1}
So y={(1,1),(2,1),(3,1)} like that ?
R = that
broken cave
Sorry
lilac flame
i didn't check but prolly right
broken cave
Yes R is that
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broken cave
.reopen
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broken cave
u missed some ponits
It can also be a number less than 1?
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late laurel
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late laurel
google says this question doesnt make sense
ionic pendant
maybe they mean the normal vector?
that's not unique but at least it has a unique direction
main sigil
its quite a different thing though
i think its quite safe to just return this question to the teacher or whoever gave you that
because its nonsene
might be a typo, but its a non-obvious one
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autumn lantern
I have to find the domain for this equation
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I have to find the domain for this equation
autumn lantern
This is the solution given in the book:
I have graphed the inequalities, and gotten most of the answer, but I don't understand why there's a -1 + ... in the domain? Should it not just be -{sqrt[1-(x-2)^2]} < y?
gray rock
it's from here
so we have (y+1)^2>1-(x-2)^2
then it follows y+1 > sqrt(1-(x-2)^2)
and then taking that +1 on the otherside of the inequality results in -1+...
autumn lantern
Oh! I was solving the wrong circle, thank you
gray rock
np
autumn lantern
.close
fast ridge
context: I'm doing proofs over graphs
hey guys, I want to prove that an edge v-w is st-efficient if and only if dist(s, v) + weight(v, w) + dist (w, t) = dist(s, t)
fast ridge
so I'm trying to prove the first part
edge v-w is st-efficient implies dist(s, v) + weight(v, w) + dist (w, t) = dist(s, t)
and I'm having a hard time
on the other hand, is there a channel for graphs?
stoic garden
!occupied
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@fast ridge Has your question been resolved?
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granite pivot
Math with a little motivation(someone give me what to know for the algebra 1 eoc)
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Math with a little motivation(someone give me what to know for the algebra 1 eoc...
@granite pivot Has your question been resolved?
empty orchid
Math with a little motivation(someone give me what to know for the algebra 1 eoc...
Hop off grow your garden 🥀
full dock
Math with a little motivation(someone give me what to know for the algebra 1 eoc...
no way you are playing that grow a garden 💀
granite pivot
No no I play to make pretty garden 😊
empty orchid
Anyways, you should probably send your syllabus
granite pivot
What’s that
empty orchid
Or curriculum
granite pivot
What’s that
empty orchid
Brother 💀
empty orchid
Ok
empty orchid
Ok!
empty orchid
How you doing on the practice
empty orchid
With word problems
Could you send an example?
tepid hamlet
granite pivot
granite pivot
If it is linear, what should you do?
The thing is I don’t know what linear means
Like
Nobody ever told me
bright oracle
It means the graph is a straight line
granite pivot
Oh
bright oracle
So it’s increasing at a constant rate
Yes
granite pivot
Have you covered y = mx + c?
What does y =? M X + b!!
I love ymxtb
I’m so cooked
I’m going to retake this class in 8th grade
bright oracle
So it means that every hour, it changes by the same amount
granite pivot
Yes yes I know that
void dew
just find slope to find the rate then use that till the time needed for the problem
0.6 feet an hour
so the answer is 4.5 feet
@granite pivot
astral orchid
who tf wants my help
void dew
who tf wants my help
no one byut i cant havew it
void dew
buddy it is 4.5 feet
granite pivot
Y2-y1/x2-x1?
void dew
yes kid 0.6 ft per hour
granite pivot
I need to know how to do it
astral orchid
Y2-y1/x2-x1?
yes but u should be prepared for trianglex/triangley
granite pivot
(Could be 8th)
astral orchid
I in 7th grade 🤑🤑🤑🤑
ban there ass
astral orchid
<@&268886789983436800>
fair bison
Okay he says he's 13+, so nothing to do here
granite pivot
fair bison
Let's go back to helping with the question
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@granite pivot Has your question been resolved?
granite pivot
No
small marsh
thought so
granite pivot
r we both stressing over algebra eoc
And yes
small marsh
whens urs
granite pivot
We have science and social studies Wednesday because we have church and they don’t require like
Skills
Just knowledge
small marsh
if i were u id study mostly graphs/graphing and different methods of solving linear/exponential/quadratics
granite pivot
I know most of that then
small marsh
can i give u one of the biggest tips i found outmyself
small marsh
4?
small marsh
ok
granite pivot
Yes
small marsh
did she teach you the equation for that
granite pivot
No
granite pivot
But I just plot what looks nice
small marsh
ok
so basically
when you are given x and y values and you need to find out the equation/function
there is a special tool that hands you the line + equation
its different between linear exponential and quadratic
btw
r u using desmos or like a physical calculator for the test
granite pivot
Physical but desmos is available
granite pivot
Okk
small marsh
so first, with the x and y values
create a table and plug them in
then from here put in the numbers
im going to use a random thing for mine
1 sec
granite pivot
Ok ok
small marsh
lets say for this
granite pivot
Ok
small marsh
so the equaition looks something like this in order to turn the points into a line (linear)
granite pivot
Is this the one where you find where it repetas
small marsh
small marsh
to do the 1 under the things, its the top left key
usually the esc key i think
i lied
the
its
just 1
so like
y then press 1
and it makes the under
then for the squiggly
small marsh
shift + `
granite pivot
A calc
small marsh
do it on desmos
small marsh
and after you do that, you get something like this
it tells you the average line for the graph
and for real linear equations (rather than just random dots) it shows the real equation with the y intercept and slope
then here are the equations for exponential and quadratic
quadratic'
exponential
the exponential one isnt always totally correct because it doesnt take into consideration the asymptote
granite pivot
The asymptote I forgot
small marsh
but they are similar
granite pivot
Know the word forgot the meaning
small marsh
its the minimum y
see how it stops a little under 4?
then becomes straight
thats where the asymptote is
granite pivot
Ohh ok ok
small marsh
thats basically all i got rn
granite pivot
Ok ok tyyyy
small marsh
solving is pretty easy when your given an equation though
just abuse desmos i cant lie
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coarse lark
help
dapper swift
no, because -4 is a vertical translation of 4 down
ebon dagger
To get the vertical assymptote, you let whatever is in the logarithm equal to zero
dapper swift
that doesn't affect the vertical asymptote
you would need a horizontal translation/dilation to affect a vertical asymptote, to move it left or right
dapper swift
that doesn't affect the vertical asymptote
if you move a vertical line from y = -infinity to y = infinity up or down, nothing changes
coarse lark
ohhh if it was verticle it would be 2ln(x-4)
ebon dagger
Yep
coarse lark
okay so then
dapper swift
ohhh if it was verticle it would be 2ln(x-4)
now the asympote would be x = 4 mhm
coarse lark
how do i draw that graph
dapper swift
ohhhh
dapper swift
then translate it down by 4
okay then
importantly you'd need to solve 2 ln(x) - 4 = 0 for y = 0
the x-intercept
dapper swift
what about y intercept
doesn't exist
coarse lark
but
dapper swift
ln 0 is not 0
dapper swift
ln 1 = 0
odd sky
U will get y = 0 at x = e^2
dapper swift
theres only x intercept
for ln(x), yes
if you have ln(x + k) where k is positive, the vertical asymptote would now be x = -k
so it would have one
blissful prawn
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blissful prawn
as a rough estimate, how many marks have I probably got with this paper? It's non calculator section A Paper /16 marks
GCSE level paper
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@blissful prawn Has your question been resolved?
river wasp
can you make your writing neater
like, write on spare paper first
especially 4th pic, if i were grading that
i would get a headache
zealous mortar
You are correct on all of them but you reasoning is false for the fourth problem.. aka u got lucky
blissful prawn
You are correct on all of them but you reasoning is false for the fourth problem...
Okay
What mark do I get out of /16?
@zealous mortar
zealous mortar
Idk depends if ur teacher
zealous mortar
If I was ur teacher i would have given a 8-10
zealous mortar
Which grade
zealous mortar
Ye
It is again as I said depends if ur teacher wants to accept ur question able reasoning
blissful prawn
Do you know about mathematics? What Mathematics have u done?
Can u tell me
What mathematics did u do
?
zealous mortar
Completed 10th grade,
zealous mortar
Yep
zealous mortar
Just getting introduced to it
blissful prawn
zealous mortar
How is this coherent to the topic?
blissful prawn
river wasp
it's funny. laugh.
blissful prawn
Lol
forest coral
Hahahaha
zealous mortar
😶
blissful prawn
Hey @zealous mortar
zealous mortar
Are u learning for jee??
Will be soon
zealous mortar
Never heard of it
zealous mortar
Do u perhaps means equations with two variables?
forest coral
Yt
blissful prawn
@zealous mortar
Do u know all these
Algebra: Linear equations, quadratic equations, polynomials
Geometry: Triangles, circles, coordinate geometry
Mensuration: Surface area and volume
Statistics & Probability: Basic concepts
Trigonometry: Introduction to ratios and identities
Arithmetic: Number systems, ratios, percentages, profit & loss, etc.
zealous mortar
Excel at them
blissful prawn
You are good at all of them?
blissful prawn
Not really
How do I get good at algebra?
Did u scores well in Class 10 Math in India
?
zealous mortar
Watch a video ig . Don't let ego get thinking it's easy , it is crucial . It's taught in 7-8grade
zealous mortar
Did u scores well in Class 10 Math in India
91
blissful prawn
91%?
forest coral
Can u teach me them?
I am not a mathematician.
I don't know the formal definition and stuff
spiral ocean
This question is on the introductory unit for integrals. Prove that
[ \int_0^x \left( \int_0^u f(t) dt \right) du = \int_0^x f(u)(x-u) du]
(Hint: Express the integral on the right-hand side as the difference of two integrals. Then show that both sides of the equation have the same derivative with respect to ${x}$.)
solid kilnBOT
k
full dock
The pulling out x?
spiral ocean
ye
full dock
Well you integrate with respect to u so I think it’s fine
dapper swift
so in this case x is a constant mhm
spiral ocean
why is that tho
dapper swift
Well you integrate with respect to u so I think it’s fine
.
thorn bay
and vice versa
it's part of the notation, otherwise it would say u(x) or have a written comment
spiral ocean
so u is an arbritary independent varible?
thorn bay
so u is an arbritary independent varible?
not sure what "arbitrary" here means.
thorn bay
Not sure it's helpful to think about variables as dependent or indepehr, im thinking about your question
spiral ocean
if u is dependent on x, then i dont think we can pull it out, ya?
thorn bay
reason im reluctant is because in calculus we have the implicit function theorem so often
thorn bay
if u is dependent on x, then i dont think we can pull it out, ya?
correct
i think its more helpful to think about dependency vs constant, not dependency vs independence
thorn bay
du/dwhat?
spiral ocean
any variable?
spiral ocean
you might ask, well, d5/d5 doesnt make sense ,
ye. thats what im about to point out...
thorn bay
true, the difference is whether its a constant AS FAR AS variable x is concerned
not whether it changes in any way
thorn bay
example
let S be the time i spend on cooking on any given day, T be the free time I have that day, Y be the mass of a clump of radioactive material sitting in a lab in France
then dS/dY=0
but dS/dT != 0
actually these are random variables so poor choice of examples
but the point is the quantities are not influencing each other in any way
thorn bay
with respect to that variable yes
spiral ocean
ah ic
thorn bay
this is kind of like partial differentiation, except there you temporarily pretend there is no relationship in anything except each variable at a time, even if it's not true
del/del x f(x,y) holds y constant , del/del y f(x,y) holds x constant
spiral ocean
so by integrating in the u world
and x is not influenced by u
i can pull it out
of the integral?
thorn bay
yes, but if you have a relationship like x=cos u, you cannot
thorn bay
🎉
spiral ocean
so in this question
x is not a function of u
or influenced by u
so it remains fix when i integrate using u
as by moving u around, x doesnt change
thorn bay
because it acts like a number like -4
if you didnt want that implication the writer would write something like x(u) for x, or u(x) for u
spiral ocean
i see, isee
thorn bay
or sometimes its clear from context, like
$$
\begin{cases}
\dot{x} = 3x + y \
\dot{y} = 2y + t
\end{cases}
$$
solid kilnBOT
gfauxpas
thorn bay
here the implication is that x is x(t),y is y(t)
because what else are you differentiating x and y wrt?
thorn bay
yes
spiral ocean
damn
thorn bay
spiral ocean
.close
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cinder cape
I have found a "proof" for the alternating series test but somehow I managed to do so without using two of the main critical conditions. Thing is I cant see where I went wrong so I will write it here for you to judge.
cinder cape
First we choose an epsilon
then consider the following
$|a_m - a_{m-1} + a_{m-2} - a_{m-3} + ... + a_{n+1} - a_{n}|$
solid kilnBOT
CherryMan
bright quarry
remove the space before the $
solid kilnBOT
CherryMan
cinder cape
then we are given that a_n converges to 0
that means that a_n is contractive for some lambda
thus
$\leq |a_{n+1}-a_n|(1+\lambda^1 + \lambda^2 + ... + \lambda^{m-n-1})$
solid kilnBOT
CherryMan
bright quarry
**CherryMan**
this should be - a_{m-3}
cinder cape
ah
my mistake
if i edit it now tho its gonna be pushed to the bottom
anyways
$\leq |a_{n+1}-a_n|\frac{1}{1-\lambda}$
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CherryMan
cinder cape
$\leq\frac{\lambda^n}{1-\lambda}|a_2-a_1|$
solid kilnBOT
CherryMan
cinder cape
now if we take m,n > N
where N is large enough
then this equation can be lesser than the given epsilon
thus
we proved that the alternating series is cauchy
and thus convergent
now wheres my mistake cus i didnt use the fact than a_n converges to 0, nor did i use that it is monotonic
bright quarry
then we are given that a_n converges to 0
?
cinder cape
?
thats the givens for the alternating series test
an converges to 0
an is monotonic decreasing
prove the alternating series converges
bright quarry
now wheres my mistake cus i didnt use the fact than a_n converges to 0, nor did ...
"cus i didn’t use the fact that a_n converges to 0"
cinder cape
"cus i didn’t use the fact that a_n converges to 0"
i only used the fact that it converges
bright quarry
that means that a_n is contractive for some lambda
what is "contractive"
cinder cape
basically
a contractive sequence is such that
$|a_{n+2}-a_{n+1}|\leq \lambda|a_{n+1} - a{n}|$
bright quarry
oh
solid kilnBOT
CherryMan
bright quarry
but 0 < lambda < 1?
bright quarry
oh ok
cinder cape
ok maybe i got some specifics wrong
but the proof would still hold
like the geometric sequence is prolly
$|1+\lambda^2 + \lambda^4 + ... + \lambda^{2(m-n-1)}|$
solid kilnBOT
CherryMan
bright quarry
how do we know convergence implies contractive?
bright quarry
contractive sequences are cauchy and thus convergent but we don’t know that all convergent sequences are contractive
contractive seems to be a "fast" cauchy sequence
cinder cape
ok thanks!
bright quarry
contractive is stronger than cauchy
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balmy basin
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balmy basin
Why is there a sqrt
I know that typically the 2 norm means you take the sqrt of the sum of squares
wooden plover
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bright quarry
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drowsy moss
.close
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static nest
hello I unable to request help due to the channel for step 1 is missing even after activating it
static nest
heres a photo
ionic pendant
this is your help channel
static nest
oh crap
tiny elm
by messaging help-38 you created the help channel yea
static nest
sorry then
ionic pendant
it doesn't have to be help-0, it can be any number
tiny elm
whats ur math question
static nest
I'm new to this
ok then
basically this
and also this
I apologize
I personally tell the diffrence between reduce row and row echelon form
these are the answer in the text book for odd number
and my professor said for the linear equation I only need to do
31,35,37
thorn bay
and my professor said for the linear equation I only need to do
31,35,37
it's not clear what you're asking us
static nest
sorry I want to understand row-echelon form and reduce row-echelon form for the first photo which is question 27-30
and I also want to understand Gaussian elimination,
back-substitution and Gauss-Jordan elimination.
thorn bay
so first of all, reduced row echelon form is a type of row echelon form
like how all ducks are a type of bird, or all triangles are polygons
static nest
ok then
thorn bay
every matrix of real or complex numbers has a reduced echelon form, which is not unique
involving doing elementary row operations on the matrix, EROs, have you seen that term
thorn bay
there are three ways to change a mtrix using an elementary row operation
thorn bay
interchange two rows
multiply a row by a non-zero scalar
replace a row with that row + a scalar multiple of another row
static nest
whats a scalar
thorn bay
a constant real number. or complex number, depending on context
static nest
oh ok then
thorn bay
importantly, if a matrix represents a system of equations, an ERO produces a system of equations with the same solutions (or lack of solutions) as the original
so it's beneficial to "simplify" the matrix to see the solutionjs more easily by performing EROs.
if you simplify it partly, you get row echelon form. this is not unique.
if you simplify it even more, you get reduced row echelon form. this is unique.
static nest
So these problems needs to be simplify
thorn bay
yes. here are the rules for row echelon and reduced row echelon
echelon is based on a word (Latin? Greek?) for ladder or staircase
static nest
ok then
thorn bay
all rows that are all 0s have to be at the bottom
the first non-zero entry of every row (counting left to right) should be below the first non-zero entry of the row above
static nest
yeah thats the confusing part I don't get
thorn bay
let me make an example
first check: are all non-zero rows at the bottom? well there aren't any all-zero rows, so that's not a problem
first row: what's the first non-zero entry (pivot) of the first row?
static nest
that would be one
thorn bay
position (2,2)
right?
that's to the right of the row above it
third row, what's the position of the pivot? not the number, the position
static nest
question: wouldn't it be neither since buttom isn't all zero
thorn bay
doesnt have to be all0, it just has to be: IF there is a row that's all 0, it's last
thorn bay
what position?
static nest
it's in column 4
thorn bay
which row which column
static nest
privot 7
row 3 column 4
thorn bay
yes
static nest
it's to the right now 1
row 2 column 2
thorn bay
and (3,4) is to the right of (2,2) which is to the right of (1,1)
so it's in row echelon formk
static nest
yeah thats the confusing part for one of the question
for 29 it seems to meet all the requirement but the text book said it's neither
thorn bay
why the confusion? you just explained to me why it's in row echelon formk, basically
thorn bay
for 29 it seems to meet all the requirement but the text book said it's neither
oh, it could be your book is demanding that row-echelon form has positive 1 for the pivot
and not just any non-zero number
that's an ... annoying convention, but some books do that
static nest
oh so I doesn't meet it because the number is less than zero
does this mean it depends on my professor
thorn bay
oh so I doesn't meet it because the number is less than zero
no, because the number is not one
static nest
wait didn't the last problem have the number 7
thorn bay
does this mean it depends on my professor
yes, you should ask if row echelon form for your professor's convention has to have a 1 for the pivot or if it can be any non-zero number
thorn bay
wait didn't the last problem have the number 7
yes, I was going by the definition that didn't require 1
there are two definitions and they're not equivalent
thorn bay
between row echelon and reduced row echelon?
static nest
between 1 or the more than 1 in the row or colmun
thorn bay
you have to see what the book or professor wants as the definition
static nest
I can send to you right now if you want
thorn bay
for reduced row echelon,
the pivots have to be 1,
and all COLUMNS with a pivot has to have 0 everywhere other than the pivot
static nest
I tried reading it but the examples are hard to understand
thorn bay
so for this one
if your book wants a leading coefficient of 1 for row echelon
you would need to replace row 1 with -1*row1
static nest
gotcha
thorn bay
[
\begin{bmatrix}
1 & -2 & -1 \
0 & 1 & 0 \
0 & 0 & 1 \
\end{bmatrix}
]
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gfauxpas
thorn bay
then you get this. is it in reduced row echelon? let's see
the first column has a pivot at entry (1,1), and every other entry in the column is 0, so that's good
for the second column, what are the pivots?
static nest
what if pivot (2,2) was -3
does this mean it wouldn't count has a row echelon since it's below 0
thorn bay
if (2,2) was -3 , whether it counts as row-echelon depends on whether your book needs the pivot to be 1, or if it can be any non-zero number
whether it's negative or positive isnt the point
static nest
I thought I was starting to understand but now I'm more confuse
gimmie sec let me see what the text book say about it
thorn bay
definition 1: row echelon form can have the pivots be any non-zero number.
definition 2: row echelon form has to have the pivots be 1
the definitions are not interchangeable
static nest
here it is
I don't really understand it
I'm guessing the book only excepts
I guess I'll put both for question 29
I believe question 30 is a reduce row echelon
hello is thier anyone
hey bro I'm gonna leave now cause it seems your unavalible at the moment thanks for your help
.close
static nest
hello is anyone avaliable
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hello is anyone avaliable
frosty birch
Someone help me simplify this using properties
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Someone help me simplify this using properties
@frosty birch Has your question been resolved?
runic estuary
I've been trying to understand this person's statistical inference. I believe he's using a maximum a posteriori estimation. But I don't exactly follow the estimation. Is the reasoning flawed? Is there a way to formally write this out?
Here's the original context https://knownandstrangethings.video.blog/2019/07/23/a-note-on-the-fine-tuning-argument/
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I've been trying to understand this person's statistical inference. I believe he...
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left oriole
what text is this from, "probability for poets"?
there's a lot of unclear stuff here, like e.g. in the first paragraph they seem to be suggesting that a uniform distribution on $\mathbb R$ exists
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Bungo
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runic estuary
runic estuary
there's a lot of unclear stuff here, like e.g. in the first paragraph they seem ...
if its unclear, im not sure what other context would be useful, try scrolling thru the bottom section here to get an indepth feel if youre curious
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gilded juniper
it has been a long time since i did much statistics at all, so i had to go back and review a bit
as bungo said, there is no canonical uniform distribution on R, so that kind of sounds like nonsense
but sweeping that under the rug, MAP estimation with a uniform prior is just maximum likelihood estimation
anyhow, basically you have a prior distribution $p(\theta)$, and the posterior is given by
$$p(\theta,|,x) = \frac{p(x,|,\theta)p(\theta)}{\int p(x,|,\theta)p(\theta)d\theta}$$
which is just
$$p(x,|,\theta)p(\theta)$$
up to a normalization constant, aka your likelihood function times your prior distribution
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suremark ꙮ
gilded juniper
in bayesian statistics this is your new distribution for theta, in MAP you just maximize p(x | theta) p(theta) over theta
and if theta is uniformly distributed then p(theta) is a constant and we can drop it when maximizing the RHS
all that said, the article seems like nonsense tbh, one sample does not an estimation make, you would need to sample from many "universes" to have any justification that this approaches the "true" distribution, and moreover things in nature are not normally distributed because of "natural processes", they are normally distributed due to the central limit theorem, which more or less says when you add many independent factors together things tend to a normal distribution
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runic estuary
all that said, the article seems like nonsense tbh, one sample does not an estim...
Okay, great. I understand all your explanation so far. Can you expand on your critique about sample size of 1? Does that mean the maximum MAP is no longer reliable or something?
I'm trying to figure out how the author is applying the MAP stuff to his universe example.
runic estuary
Mistyped there
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@runic estuary Has your question been resolved?
runic estuary
@fervent thorn
dire elm
.
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west saddle
I'm trying to figure out how the author is applying the MAP stuff to his univers...
donno how accurate, but i think the general idea is just that with very little data:
this is our best estimate
intuitively, say like if you only know that some random marsian is 5 cm tall. We can guess that marsians have an average height of 5cm because everything else would make less sense to guess.
I don't think they're trying to argue that the estimator would be good in any sense, but ig it makes sense to me intiutively idk :3
but idk where the normal distribution popped up from
runic estuary
I don't think they're trying to argue that the estimator would be good in any se...
is the MAP estimator reliable with a sample size of 1?
runic estuary
but idk where the normal distribution popped up from
i believe they're using the central limit theorem to argue for the normal distribution assumption
west saddle
is the MAP estimator reliable with a sample size of 1?
i mean you're not going to reliably estimate anything with one data point, there's just no getting past that (unless the standard deviation is known to be something like 0). It's just c is just the value that's more likely than any other to be mu given your data.
west saddle
i believe they're using the central limit theorem to argue for the normal distri...
oh think they were just arguing that "a lot of shit in nature has a normal distribution", And assuming that whatever they're looking at does too.
wait im just looking at the context 🤣
runic estuary
i mean you're not going to reliably estimate anything with one data point, there...
is there a way to estimate the error probability? im thinking with a larger sample size, the error probability when using MAP decreases
runic estuary
oh think they were just arguing that "a lot of shit in nature has a normal distr...
yeah i'd guess loads of nature has normal distributions due to the central limit theorem. how would the central limit theorem be applied here to argue for the normal distribution? im trying to think
west saddle
is there a way to estimate the error probability? im thinking with a larger samp...
idk, someone else might be able to answer better :3
but the jump from assuming that any real value has equal chance of being the mean to a normal distribution with low variance based off of one data point is kinda wild.
I feel like the whole back and forth can just be summed up as:
first guy:
- the chance that the universe bears life is so unlikely! This is best explained by god!
second guy:
- well since the only universe that we know of has life in it. That probably means that universes in general tend to have conditions that favours life!
west saddle
idk, someone else might be able to answer better :3
but the jump from assuming ...
the error would prolly depend on the variance, which they want to assert is small for some reason
runic estuary
I feel like the whole back and forth can just be summed up as:
first guy:
- th...
yeah that makes sense, what about the assumption of normal distribution & the central limit theorem? i saw they were arguing the assumption of normal distribution was reasonable on the basis of the central limit theorem
west saddle
yeah that makes sense, what about the assumption of normal distribution & the ce...
i dont think they mentioned CLT at all XD
and i really would not know how you'd figure out if CLT should apply to physical constants "across different universes"
idk, but idk how you'd get a good idea of how the value physical constants get generated.
runic estuary
idk, but idk how you'd get a good idea of how the value physical constants get g...
hmm, lets suppose they did. what are the conditions of the clt to apply? isnt it like independence or something. how could you apply it here
west saddle
hmm, lets suppose they did. what are the conditions of the clt to apply? isnt it...
Something like each physical constant (or whatever) we’re interested in is a sum/average of a shit tonne of things that don’t depend on each other.
runic estuary
Something like each physical constant (or whatever) we’re interested in is a sum...
Can you elaborate? Not sure i follow
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noble nest
!helpers
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To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
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halcyon rampart
,tex put $$ 2^x = u $$
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halcyon rampart
if you know how to solve quadratics , you can solve this
so do you know how would you would solve this ?@fresh igloo
void dew
$u^2-5u+4=0$
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ppq#7826
void dew
$u = a -5 = b + 4=c$
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ppq#7826
halcyon rampart
what are you doing lol
halcyon rampart
**ppq\#7826**
$$ u^2 -4u -u + 4 = u(u-4)-(u-4) = (u-1)(u-4) $$
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halcyon rampart
$$ 2^x = 1 $$
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quasi wigeon
**grey**
u just need to put it in a calc right?
log
log(2)=4
right
$log(2)=4$
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Tan
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south
dapper swift
u just need to put it in a calc right?
no, take log base 2 on both sides
what you wrote isn't correct
quasi wigeon
oh
quasi wigeon
no, take log base 2 on both sides
but im correct right
quasi wigeon
u just need to put it in a calculator
dapper swift
u just need to put it in a calculator
ah yes
dapper swift
but you need to put the right thing in
forest needle
Somebody asked a question yesterday or the day before and it took me quite a while to solve it.
I don't remember which channel or who asked this question
gray sun
Did you just react to your own message 😭
runic estuary
looks like it 😆
simple rock
i didn't read entire thing, i just read the pinned msg and in that it was x^(2i) but whatever leave it, he will tell if he still cares.