#help-42
calm coralBOT
jolly plover
jolly plover
wait how is chain rule applied here? i thought i do power rule after that
velvet osprey
wait how is chain rule applied here? i thought i do power rule after that
you use the power rule to differentiate the outer function (the cube root) and formally the chain rule means you also need to multiply by the derivative of (x+4)
jolly plover
so in this case when i have (x+4)^1/3
chain rule says that i can use it if theres a function that i can derive inside a function?
velvet osprey
but d/dx (x+4) is just 1
chain rule says that i can use it if theres a function that i can derive inside a function?
this wording is not good
jolly plover
yeh i confused sorry . 😅
english not my first langugage
can you correct my word? i tend to understand by words then seeing examples
vital blade
if there are multiple functions inside one another ig
velvet osprey
english not my first langugage
what is your first language?
jolly plover
filipino
vital blade
viladimiro putinoooo
velvet osprey
what?
anyway...
the chain rule tells you how to take the derivative of a composition of two functions,
assuming that you already know the derivatives of each one
i.e. the chain rule tells you how to get the derivative of f(g(x)) when you know f'(x) and g'(x)
this is much easier to phrase in symbols than in words
at best you can call f the "outer function" and g the "inner function"
leaden marsh
“you crack the shell then the nut inside” 🤓🤓
velvet osprey
?
jolly plover
i see this
i think of it this way
f = (x+4)^1/3
g = x+4
f' = 1/3(x+4)^-2/3
g' = 1
therefore
1/3(x+4)^-2/3 * 1
am i getting it right
?
jovial sedge
wdym derive
leaden marsh
wdym derive
differentiate
jovial sedge
its called differentiation
jolly plover
sorry new to it
velvet osprey
^ yeah english is dumb like that
you take the derivative, but the verb is to differentiate
leaden marsh
I never fully understood the chain rule in that form lol
jolly plover
the f is just the ^(1/3)
ok this make sense now
so when i differnetiate it
i get 1/3(x+4)^-2/3
and i can put it down in denominator and get
1/3cuberoot(x+4)^2
how do i use the type to image equation maker bot
leaden marsh
$\frac{1}{3\left(\sqrt[3]{x+4}\right)^2}$ like this?
potent lotusBOT
blahaquil
velvet osprey
both $\frac{1}{3} (x+4)^{-2/3}$ and $\frac{1}{3(\sqrt[3]{x+4})^2}$ are correct
potent lotusBOT
Ann
jolly plover
**Ann**
thiss
ohh okay thanks so much i get it now
t hank you guys
blessed day ❤️
leaden marsh
some ppl think the second one is more simplified for a reason I will never understand!!
jolly plover
some ppl think the second one is more simplified for a reason I will never under...
hahahah i just hate negative exponents taht why
leaden marsh
fair
humble zealot
hello, i have a question about the fundamental theorem of abelian groups
humble zealot
every finite abelian group is isomorphic to the direct product of cyclic groups, each one with order the power of a prime number
and the primes dont need to be distinct
so Z4 should be isomorphic to Z2 x Z2
but gcd(2,2) is not 1, so thats not possible
what am i getting wrong?
here for example it writes Z4 x Z7 x Z5 as Z2 x Z2 x Z27 x Z5, but Z4 is not isomorphic to Z2 x Z2
similarly Z27 cannot be decomposed in Z3 x Z9 because gcd(3,9) is not 1
glass heart
you are misunderstanding the theorem
Z4 is already a cyclic group with the power of a prime
humble zealot
Z4 is already a cyclic group with the power of a prime
yea but it says that the primes dont have to be distinct
glass heart
and?
Z4 = Z4 is already such a decomposition
the fundamental theorem does not say that all such decompositions are isomorphic
humble zealot
the fundamental theorem does not say that all such decompositions are isomorphic
okay, but why then is Z4 written as Z2 x Z2 in the pic?
glass heart
no
calm coralBOT
quaint sapphire
calm coralBOT
fickle hearth
quaint sapphire
ah yes thank you
calm coralBOT
@quaint sapphire Has your question been resolved?
sleek dust
Can someone explain to me why the 2x multiplied by the cosx+2xy is 2xcosx + 2x^2y and not 2xcosx + 4x^2y
velvet osprey
someone seems to have fucked that part up
sleek dust
So it is 2xcosx +4x^2y?
velvet osprey
appears that it should be, yes...
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shrewd dock
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shrewd dock
Can someone explain to me how we are finding these solutions
I found r =0 one and r=1 and r=-1
so there is 3 more solution I did not find
leaden thunder
$r^4 - 1 = (r^2)^2 - 1$
potent lotusBOT
riemann
leaden thunder
use difference of squares again and factor some more
shrewd dock
Can you elaborate please
leaden thunder
Can you elaborate please
which part
shrewd dock
**riemann**
here please
potent lotusBOT
riemann
leaden thunder
r = a and x = 2 and y = 2
shrewd dock
Yes ofc I got this haha
But ((r^2)^2)-1
then I rename r^2 as 'a'
so it becomes (a^2-1)
and use difference of squares
calm coralBOT
@shrewd dock Has your question been resolved?
noble narwhal
hello, i need to prove that I2 is maximal
calm coralBOT
hello, i need to prove that I2 is maximal
noble narwhal
maybe i can start by proving A\I2 is a field?
calm coralBOT
@noble narwhal Has your question been resolved?
noble narwhal
what field is it
i dont know
velvet osprey
including X in the ideal you're quotienting by means that X and all powers thereof become 0
that already leaves not a lot of elements
calm coralBOT
@noble narwhal Has your question been resolved?
tired locust
quick question
calm coralBOT
quick question
fringe reef
no
fringe reef
but then how would i do d
when he enters the water, the height is 0
tired locust
ok
fringe reef
0 = -d^2 + 3d + 4
so solving this would give you 2 possible solutions, out of which you'll need to pick 1
but first solve it
fringe reef
o so its just 5
why 5?
tired locust
no
i tghought cause the toal distnace but
no
what would it be
@fringe reef
<@&286206848099549185>
tulip spear
i tghought cause the toal distnace but
its just asking for the zeroes fr
tired locust
ok
tulip spear
problem is, can you have negative distance
tired locust
its the vertaixx right
tulip spear
yeah
tulip spear
e is the y-coord of vertex
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cinder mural
I’m not very great at exponents or logarithms, I need help on 2e^2x = 97
tulip spear
I’m not very great at exponents or logarithms, I need help on 2e^2x = 97
divide both sides by 2
ln both sides
divide by 2 again
cinder mural
Wait so divide by two to get e^2x = 48.5
And then shouldn’t I put it into a log equation?
vague bison
Wait so divide by two to get e^2x = 48.5
wdym? e²x = 48.5??? plz write clearly (with LaTeX)
tulip spear
And then shouldn’t I put it into a log equation?
take ln both sides yeah
just put parenthesses where you mean to so you dont confuse ppl
e^(2x)=48.5
cinder mural
I don’t know how to use the commands
And I figured it out on my own with Google anyway
.close
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royal smelt
does this setup look right before i actually go through all the integration
calm coralBOT
does this setup look right before i actually go through all the integration
@royal smelt Has your question been resolved?
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@royal smelt Has your question been resolved?
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fading thunder
how should i go solving this problem
calm coralBOT
how should i go solving this problem
fading thunder
this is in my vector chapter of my textbook
velvet osprey
what are u and v
fading thunder
whered you get the 2 eqaution from
sweet pike
It's given that xu +yv =44j
xu= 7xi+8xj
velvet osprey
^
sweet pike
yv= 2yi-4yj
And rhs has 44j, thus i has the coefficient of zero
We'll compare the coefficients
fading thunder
so i would start by stating x(7i + 8j) + y(2i-4j) = 44j ?
sweet pike
yeah
fading thunder
and then from here i would put the i coords to 0 since they arent on the rhs?
fading thunder
right but how do i get 2 equations from this
sweet pike
so on comparing the coefficients of the coordinate you can make the eqns
Like this: (7x +8y)i + (8x-4y)j = 0i +44j
calm coralBOT
empty lark
Can you solve it? 3 ln(x + 1) = -ln(2x - 1)
leaden marsh
ln(y^x) but yea
sweet pike
I meant that yeah
empty lark
Hey so you could use the property: xlny = ln(y)^x
Thank you, I understand.
sweet pike
So the eqn will become (x+1)^3 = (2x-1)^-1
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ripe jacinth
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ripe jacinth
can anyone tell me why is 2(wcsctheta) where w = mg is wrong
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@ripe jacinth Has your question been resolved?
simple violet
can anyone tell me why is 2(wcsctheta) where w = mg is wrong
it should 0.5(w cosec tetha) right?
ripe jacinth
it should 0.5(w cosec tetha) right?
yea from the book
simple violet
wdym? as in that's the correct answer or?
ripe jacinth
wdym? as in that's the correct answer or?
the correct formula for that
simple violet
Yeah, you've made a small error in subjecting. the Tl and Tr are equal in this case so let them be both equal to T, then resolve upwards where T sin 0.5 + T sin 0.5 = w, so 2 T sin 0.5 = w and T = 1/2 * (w csc tetha)
in the last step you've multiplied RHS instead of divide
ripe jacinth
in the last step you've multiplied RHS instead of divide
yea i multiplied it because i assumed T_total = T_left + T_right
and since T_total = T_left + T_right are the same i multiplied it by 2
simple violet
ahh I see, small errors like this happen
ripe jacinth
and since T_total = T_left + T_right are the same i multiplied it by 2
tho i think in this part is where i got it wrong
ripe jacinth
ahh I see, small errors like this happen
what would be the correct approach after i have T_total = T_left + T_right where i have one of the side already
simple violet
what would be the correct approach after i have T_total = T_left + T_right where...
well that's not entirely correct, because you have to notice Tl and Tr are not on the same line (they are at an angle to each other) if you want to add them nicely you'd want to resolve them into one direction. in this example the best choice is upwards. so Tl upwards is Tl sin 0.5, and for Tr it would be Tr sin 0.5. now we can say T total upwards = Tr sin 0.5 + Tl sin 0.5, but we know Tr and Tl is equal! so we can say T total upwards = 2 Tr sin 0.5 = w (because w acts downards) and we end up with Tension along the rope = 1/2 * w * cosec 0.5. does this explanation help?
ripe jacinth
well that's not entirely correct, because you have to notice Tl and Tr are not o...
uh idk isn't tl upwards basically weight
simple violet
uh idk isn't tl upwards basically weight
When I say Tl and Tr I mean those drawn on the diagram and, tl and tr upwards is weight
ripe jacinth
e i still dont get where did i go wrong in T_total = T_left + T_right
simple violet
can you send a screenshot or pic of your working?
fluid cliff
ripe jacinth
can you send a screenshot or pic of your working?
sec
ripe jacinth
can you send a screenshot or pic of your working?
mossy geode
just do vector resolution gang
ripe jacinth
just do vector resolution gang
what's vector resolution
mossy geode
writing a vector in terms of two vectors in the plane
with which u can do calculation
easier
ripe jacinth
uh how would that help here
simple violet
Btw they're asking you to find the tension, not the total tension so you just want to fins Tr or Tl
mossy geode
i would suggest learning vectors for classical mechanics
calm coralBOT
@ripe jacinth Has your question been resolved?
ripe jacinth
Btw they're asking you to find the tension, not the total tension so you just wa...
wdym
isn't the question the tension of the whole wire
calm coralBOT
@ripe jacinth Has your question been resolved?
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@ripe jacinth Has your question been resolved?
wild nimbus
How do i get x ?
calm coralBOT
How do i get x ?
velvet osprey
wild nimbus
Nothing
velvet osprey
ok, let's start from the very basics then
what do you know about the angles in a triangle?
wild nimbus
All 2gether is 180°
velvet osprey
yes, their sum is 180°
now look at your diagram and in particular look at triangle ABC
do you see how two of its angles are known?
wild nimbus
B is 90 and C 65?
velvet osprey
yes
that's what the diagram says
so knowing that the angles in ABC have to add up to 180°
how much is the third angle (A)
dawn python
velvet osprey
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wild nimbus
So A is 35
wild nimbus
Then x should be 180 - (123 + 35) ?
velvet osprey
indeed
dawn python
what.
wild nimbus
.close
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velvet osprey
...
dawn python
explain
dawn python
great, now we need to track him down
velvet osprey
nope not gonna share
dawn python
that bad?
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marble sun
I'm a bit confused regarding functions
calm coralBOT
I'm a bit confused regarding functions
marble sun
If we have a function how to tell if we can always go from a input to its output
leaden thunder
it'd be easier if you had a specific function or problem
bold bear
If we have a function how to tell if we can always go from a input to its output
By definition you always can
That's what a function is
vagrant oak
for anything in its domain
marble sun
For example let's say we have a function which maps sets to 0 or 1, where it maps to 0 if the set is finite and 1 if it's infinite set
Here we have no way of going from input to output for sure
Cuz we can't count till infinity
bold bear
Putting aside the huge set theoretic ramifications that has, you can define that for any set
Either a set is finite or infinite (once you specify what exactly that means)
vagrant oak
Functions dont have to be computable
marble sun
Putting aside the huge set theoretic ramifications that has, you can define that...
You can define it, but I'm asking where you can go from a input to an output, and if we can't how can we tell if we can't
vagrant oak
Putting aside the huge set theoretic ramifications that has, you can define that...
But yeah, to be exact you cant have a function from the set of all sets
marble sun
Functions dont have to be computable
Yea so basically I'm asking this, how can we tell if a function is computable
vagrant oak
because the set of all sets doesnt exist
marble sun
because the set of all sets doesnt exist
Makes sense
But let's say from a set of all sets which doesn't include itself
To {0,1}
vagrant oak
But let's say from a set of all sets which doesn't include itself
hm
that only makes the paradox worse ngl
marble sun
How so
marble sun
Yea so basically I'm asking this, how can we tell if a function is computable
My question is really just this
leaden thunder
vagrant oak
computable in what sense exactly? Can you give an example?
bold bear
(dw about the paradox, it's besides the point)
marble sun
computable in what sense exactly? Can you give an example?
In that if we are given an input we can always find it's output
marble sun
https://en.wikipedia.org/wiki/Computable_function
Exactly these functions
marble sun
For example let's say we have a function which maps sets to 0 or 1, where it map...
This is not computable for example
vagrant oak
How so
And to answer this, let that set be called A.
Does your set A of all sets which dont include themselves include A or not?
If it doesn't include it, then A is a set which doesnt include itself and thus should be included in A. But if it is included, then A must be a set which doesnt include itself and thus shouldnt be in A.
you may read it or not, its about the paradox, not about your question
If we were able to tell for any function if it's computable or not, math would be too simple
marble sun
If we were able to tell for any function if it's computable or not, math would b...
Hmm
Hmm
marble sun
And to answer this, let that set be called A.
Does your set A of all sets which ...
This makes sense
vagrant oak
You can sometimes prove it or disprove it
marble sun
Yea that I know
vagrant oak
but there is not an easy algorithm to tell whether a given function is computable or not
marble sun
Like for specific functions there's ways to tell if it's computable or non computable
marble sun
but there is not an easy algorithm to tell whether a given function is computabl...
Yea
Is this a fact
marble sun
but there is not an easy algorithm to tell whether a given function is computabl...
Is this for sure
bold bear
It's actually quite easy to see that it's not computable, because there are statements that can't be proven (e.g. the continuum hypothesis)
vagrant oak
Is this a fact
consider the function from the set of statements to {0, 1} which maps it to 0 if false and 1 if true
wait actually that doesnt quite work...
marble sun
consider the function from the set of statements to {0, 1} which maps it to 0 if...
Yea cuz we don't know what statements are true in the first place
So that function is I'll defined
Ill*
marble sun
It's actually quite easy to see that it's not computable, because there are stat...
Hmm, wait
bold bear
It's actually quite easy to see that it's not computable, because there are stat...
Then you can take the subset of all natural numbers such that "the continuum hypothesis is true", then it will either be 0 or infinite
It can't be computed
marble sun
It can't be computed
But that's just a non computable function right?
Cant we just say it's not computable and move on?
bold bear
Well yeah that's what you asked for isn't it
vagrant oak
Yea cuz we don't know what statements are true in the first place
Yeah, i meant provably true, not true
marble sun
Well yeah that's what you asked for isn't it
I'm asking if we can tell if a function is computable or not
If we are sure it's not computable then we can put it in the non computable basket and move on right?
bold bear
Well then you can just do the same thing again
You can construct a function that's computable if the continuum hypothesis is true, and non-computable if it's false
marble sun
Ohh
marble sun
You can construct a function that's computable if the continuum hypothesis is tr...
But such a function would be inherently non computable right
bold bear
Not if the continuum hypothesis is true
marble sun
Since that hypothesis's truth value is non computable
bold bear
The continuum hypothes is either true or false, it's just impossible to say which one
So the function could be computable
marble sun
So the function could be computable
Oh
So there exist functions
Which could be computable
But we can't actually ever tell
If they are
Makes sense
Also another question I had
Regarding functions
A functions domain
What does it mean for it to be ambiguous
bold bear
Wdym?
marble sun
Like I've seen functions with domains such that not all elements in the domain are being mapped
Such a thing exists right?
bold bear
Technically no
The domain of a function f is defined as the set of elements such that f(x) exists
You can sometimes get functions that are defined on a subset of (e.g.) R
But then that subset would be the domain
sweet pike
Like I've seen functions with domains such that not all elements in the domain a...
oh you mean an into function?
marble sun
oh you mean an into function?
No I'm talking about the domain not the co domain
marble sun
But then that subset would be the domain
Hmm
bold bear
If you're talking about "can you compute that domain" then you have exactly the same problem as before
bold bear
Ah okay yes, that's what I was just saying then
marble sun
Makes sense
I guess I misread it
So domain is the exact set of elements which are mapped to the range
But this domain might be undefined
/ambiguous
bold bear
But then you can still quite easily construct partial functions with noncomputable domains if that's what you're asking about
Yes exactly
marble sun
But then you can still quite easily construct partial functions with noncomputab...
Right
Something here is making me
A bit confused
bold bear
Math tends to have that effect
marble sun
We still have computable functions which are partial
Which means their domain is undefined
bold bear
Dw about any of this too much yet though, it's the kind of thing that only starts mattering quite late into a uni degree
marble sun
But given an element we can map to the corresponding element in the range
marble sun
Dw about any of this too much yet though, it's the kind of thing that only start...
Ohh
No but I think I'm close to
Understanding it
bold bear
We still have computable functions which are partial
I can give you an example if you want of this
marble sun
I can give you an example if you want of this
Yes please
bold bear
although the domain of a partial function definitely can be defined, for example it could be defined on the integers as a subset of the reals
Okay
If the continuum hypothesis is true, then there are no subsets of the real numbers with cardinality strictly between |Z| and |R| (if you know what that means, lmk if you don't)
If it's false, then there are subsets like that (of "intermediate cardinality")
marble sun
If the continuum hypothesis is true, then there are no subsets of the real numbe...
No I am not sure what the continuum hypothesis is
marble sun
Not sure is an understatement, I have no idea about it
bold bear
If you take the set of all integers, it has size N, for some "infinite number" N
marble sun
If the continuum hypothesis is true, then there are no subsets of the real numbe...
But I think I get what ur saying
marble sun
So basically it's about the fact that we don't know if there's a intermediate infinity
marble sun
Between the cardinality of reals and the cardinality of naturals
bold bear
But like I said, this is completely irrelevant for most things so dw about it too much
vagrant oak
Which means their domain is undefined
Partial functions dont have undefined domain, they have a domain, they can be undefined at some points in their domain tho
bold bear
So then you can define a constant function on all intermediate sets
marble sun
Partial functions dont have undefined domain, they have a domain, they can be un...
Oh wait what
If a partial function is from X to Y and it's defined on a subset S of X
Then S is the domain right
Or is it X
bold bear
I think different authors say different things on that
vagrant oak
Then S is the domain right
Oh, yeah, i used wrong words
anyway the domain is still there
it's not undefined
bold bear
You would always have to specify what S is if you're defining a partial function
vagrant oak
"Some subset S" right?
If you meant undefined as in unspecified, then yeah
marble sun
Really?
vagrant oak
You would always have to specify what S is if you're defining a partial function
really?
marble sun
If you meant undefined as in unspecified, then yeah
What's the difference
vagrant oak
i dont think so
bold bear
Well otherwise you haven't defined anything
vagrant oak
What's the difference
i thought you meant undefined as in some thing that cant be defined
non-definable
marble sun
i thought you meant undefined as in some thing that cant be defined
Yea
That's what I thought
bold bear
Even if you just specify it as "some set S" and leave it as a free variable
It still has to be specified
I feel we're all saying the same things with different words
vagrant oak
Well otherwise you haven't defined anything
pretty sure that there is even a theorem which says that we cant decide whether a given partial function is total or not
marble sun
I mean the only thing we know about S is that it's a subset of some known set X
bold bear
Yes it's undecidable
marble sun
Other than that we have no info on it
bold bear
But it's still defined
marble sun
Right
vagrant oak
But it's still defined
Yeah, right, you can certainly define it
bold bear
Okay let me give you an example of a partial function
f : R -> R
f takes any integer to itself, and is "undefined" on everything else
Then the domain, or domain of definition, of f is the integers
Perfectly defined
bold bear
If f : A -> B is a partial function, you can always let S be the set of values such that f(x) exists
You can't always compute it, but it always exists
marble sun
If f : A -> B is a partial function, you can *always* let S be the set of values...
I see what u mean but isn't that circular, I mean u r defining S based on S itself
Because the definition of f(x) uses S
bold bear
No how is it circular?
That depends on how you define functions lol
But I promise it's not circular
marble sun
Ur defining S be such that f(x) exists, and f(x) is such that its domain is S
marble sun
Two different sets that happen to be equal, ... Is the same set right
bold bear
You're missing the point
vagrant oak
I see what u mean but isn't that circular, I mean u r defining S based on S itse...
f : N -> {0, 1}
f takes n to highest number in its collatz sequence
undefined if unbounded
Here S = set of all numbers whose collatz sequence is unbounded
Example of how its not circular
vagrant oak
whenever f is definable, S is definable
marble sun
I'm actually quite cooked here
What's the difference between undecidable and undefinable
bold bear
If an equation is undecidable, that means that there is no algorithm to decide it
Undefinable has meant two different things so far in this conversation
marble sun
Like can u say that the domain of the halting problem is "definable"
bold bear
- it doesn't exist, and 2. it can't exist
Yes it's definable
I don't think domain is the right word, but you can quite easy define the set of all turing machines that halt
It exists by the axiom of specification
marble sun
Ah
bold bear
But if you have a turing machine T, there is no way in general of saying whether T is in that set or not
marble sun
Makes sense
What about the domains complement
Ah makes a lot of sense actually but then
Why is it that HP is a partial function and not a total one
bold bear
Oh okay
That's just a regular function
Every turing machine either halts or doesn't halt
bold bear
Well, turing machines + inputs if you wanna define it like that, it doesn't matter at all
bold bear
Because for some turing machines we have nothing to map to
The turing machines still exist though
marble sun
what else would doesn't halt mean
The halting problem machine itself will loop
bold bear
The halting problem is undecidable, that's the whole point
There is no machine to decide the halting problem
vagrant oak
uh that machine cant exist in the first place
marble sun
uh that machine cant exist in the first place
It exists
vagrant oak
The halting problem machine itself will loop
looping means doesnt halt
vagrant oak
It's just not decidable
which machine are you talking about?
vagrant oak
It does accurately tell if a machine halts
this one?
marble sun
which machine are you talking about?
The halting problem machine
The machine which takes in another turing machine and tells if it halts or not
vagrant oak
The machine which takes in another turing machine and tells if it halts or not
this one doesnt exist
existence of this machine is an assumption
marble sun
this one doesnt exist
Wdym it doesn't exist
vagrant oak
which later results in contradiction
marble sun
The assumption is that the machine is decidable
/always halts
That leads to contradiction
But it's still a machine, but it's undecidable
vagrant oak
The assumption is that the machine is decidable
"decidable"?
Turing machines always execute algorithms
marble sun
Turing machines need not always halt
This machine let's call it H, does not always halt either, we assume it does, but that leads to contradiction
vagrant oak
The machine which takes in another turing machine and tells if it halts or not
okay so you are actually talking about a machine which only tells if a given machine halts
marble sun
okay so you are actually talking about a machine which only tells if a given mac...
Yes
vagrant oak
yeah, okay
marble sun
If the machine doesn't halt then it may say no or loop
vagrant oak
yeah, alright then
so if it loops it doesnt halt
if it doesnt loop, it halts
whats the problem?
marble sun
So my question originally was about defining the domain of the HP function
vagrant oak
the domain would still be all the TMs together with their inputs
bold bear
If you mean "domain" as in the set of all turing machines that this machine returns a value for, then you can just define that as a set
marble sun
For some of the turing machines and input pairs it loops
vagrant oak
yes, correct
loops meaning it doesnt halt
hence the function you were talking about would result in 0
marble sun
So it doesn't map to anything in its range
marble sun
hence the function you were talking about would result in 0
No
vagrant oak
what was the defn again then?
bold bear
Not that it's strictly relevant, but just because a turing machine doesn't halt doesn't mean it loops
marble sun
It would map to 0 if it correctly decides that the given input TM and input is looping, and halts
But it may not halt
marble sun
Not that it's strictly relevant, but just because a turing machine doesn't halt ...
What???
vagrant oak
I think that you are looking at whether the functiion can be effectively computed, not at whether it can be definde
marble sun
Kinda confused
vagrant oak
What???
halting can be considered as a type of instruction or sth like that iirc
not sure
bold bear
But none of this matters for the set theory. if T is some machine, you can still always define the set {turing machines x | T(x) doesn't halt} and there's no problem
marble sun
I think that you are looking at whether the functiion can be effectively compute...
Effectively computable means computable right
bold bear
What???
if a turing machine is computing the decimal places of pi, then it just keeps going and never repeats for example
vagrant oak
Effectively computable means computable right
im not really talking in formal terms here, but say yes
if im not mistaken, then you think that the function shouldnt be defined at looping machines just because we have no way to know whether a looping machine will eventually halt or not
marble sun
if a turing machine is computing the decimal places of pi, then it just keeps go...
Oof that's a good point
marble sun
if im not mistaken, then you think that the function shouldnt be defined at loop...
Yea
marble sun
It doesn't map to anything in its range right
vagrant oak
It doesn't map to anything in its range right
it does
it maps to "No, it doesn't halt"
we just dont have a way to compute the function you've defined
marble sun
Ahh
marble sun
Makes a lot of sense
Still cooked on one thing
The halting problem function is partial function right
bold bear
As you've defined it, sure
vagrant oak
how have you defined it?
marble sun
A function that maps from turing machine input pairs to whether the tm will halt on that input or not
bold bear
No that's just a regular full function
vagrant oak
yeah
bold bear
Either it halts, or it doesn't
vagrant oak
we just dont have a way to compute it for arbitrary value, its not computable
marble sun
Right
So what's a good example of a partial recursive function
A function which is computable but partial function
marble sun
Ah makes sense
marble sun
So hp function isn't partial recursive, it's in fact not even computable?
marble sun
That clears up a lot
vagrant oak
I don't see how it's recursive in any way
recursive is a slightly broader term than the recursion in the programming sense
marble sun
So recursively enumerable languages aren't computable?
Computable has to mean "decidable"?
vagrant oak
So recursively enumerable languages aren't computable?
not in general i think, but they can be
marble sun
not in general i think, but they can be
Wow that makes it even more confusing
vagrant oak
It's basically semi-decidable
if the string is valid, you can tell that in finite time
if it's not, then you can tell it only sometimes
it can be decidable in the special case when "sometimes" becomes "always"
it cant be equal, the range is different from the range of most computable functions
marble sun
I guess I'll do this on my own, thanks a lot guys @bold bear @vagrant oak !! U were a lot of help!
.close
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warm warren
suppose $X$ is a continuous RV, and its CDF $F_X$ be NOT strictly monotonically increasing, what is the distribution of $Y = F_X(X)$?
potent lotusBOT
frosst
warm warren
i cant figure out where the flat bits go
normally if F_X is strictly monotonic then its inverse is nicely defined
but when there are flat bits where do they go
nocturne frigate
suppose $X$ is a continuous RV, and its CDF $F_X$ be NOT strictly monotonically ...
cdf(y) = P(F_x(X) < y), so as long as the set of values for which your F_x is "flat" is of measure 0 it should work i think?
warm warren
is measure 0?
can't it be just a flat line midway through
im imagining a cdf like this
0, x < 0
x, 0 ≤ x < 0.5
0.5, 0.5 ≤ x < 1
x-0.5, 1 ≤ x < 1.5
1, x ≥ 1.5
nocturne frigate
yea so you have finite number of values that are "flat"
0, 0.5, 1
so it's measure 0
nocturne frigate
cdf(y) = P(F_x(X) < y), so as long as the set of values for which your F_x is "f...
my point is that this doesn't require the function to be invertible, because if you take an "inverse" with discontinuities wherever you'd have a vertical line, it will still be integrable
as long as it has discontinuities in measure 0 set of points
warm warren
ohh
ok and what happens when i have more
oh
it becomes not continuous probably
i think that's what happens
you'd need more than countably many flat bits
which i feel like will mean that you start losing continuity
worn pebble
you don't need continuity
you can show there are countably many flat bits because you can map all the flat bits to QxQ by mapping to rational endpoints of a smaller interval
warm warren
you can show there are countably many flat bits because you can map all the flat...
Can I not construct a monotonic function with uncountable many flat bits
worn pebble
Can I not construct a monotonic function with uncountable many flat bits
assuming you mean an interval [a,b] where the function is flat, no
warm warren
I can’t?
worn pebble
you can show there are countably many flat bits because you can map all the flat...
this was my construction of a injection** from all flat bits to QxQ which is countable
warm warren
I don’t get it
What do you mean by mapping to rational endpoints of a smaller interval
worn pebble
this was my construction of a injection** from all flat bits to QxQ which is cou...
take [a, b] choose any 2 rational points p, q such that a < p < q < b
map [a, b] to {p,q}
consider the function from all flat bits to QxQ
this will be injective
nocturne frigate
you can also look at this https://en.wikipedia.org/wiki/Discontinuities_of_monotone_functions
if you take just the flat bits, it will still be monotone so it cannot have uncountable number of jumps
calm coralBOT
@warm warren Has your question been resolved?
vivid sinew
Been stuck for a longg time on this need some help if possible
vivid sinew
college stats btw
found lower/upper half of data then subtracted for iqr
cutoff i just plugged into formula
old falcon
,w Quartiles[{193, 192, 191, 189, 185, 185, 183, 182, 182, 180, 179, 178, 177, 175, 173, 173, 170, 163}]
potent lotusBOT
old falcon
,calc 351/2
potent lotusBOT
Result:
175.5
you may want to try R
just a suggestion
can save you some pondering when something goes wrong
jovial dagger
IDK im dumb
vivid sinew
you may want to try R
wdym
old falcon
its a statistics programming language
yea
i believe the command summary prints all the answers to this question
helpful for checking your work
vivid sinew
not really sure how R works but thanks for the suggestion. for this one though did the wolframalpha give a answer?
i see the 175.5 thing
old falcon
it gave you the quartiles
if your work for the others was right, then you can just use these correct quartiles to correct your other work
vivid sinew
it gave you the quartiles
175.5 was also wrong though
vivid sinew
for the third quartile? haven't checked it
vivid sinew
163, 170, 173, 173, 175, 177, 178, 179, 180, 182, 182, 182, 183, 185, 185, 188, 189, 191, 192, 193
I think you mistyped a 189 twice?
old falcon
,w Quartiles[{193, 192, 191, 189, 185, 185, 183, 182, 182, 180, 179, 178, 177, 175, 173, 173, 170, 163}]
potent lotusBOT
old falcon
removed one of the 189
vivid sinew
,w Quartiles[{163, 170, 173, 173, 175, 177, 178, 179, 180, 182, 182, 182, 183, 185, 185, 188, 189, 191, 192, 193}]
potent lotusBOT
old falcon
yea
old falcon
it would
viral abyss
calm coralBOT
viral abyss
why is not 156
viral abyss
also how did you reach that conclusion
linear pair and that arcs are double the angle
tulip spear
linear pair and that arcs are double the angle
not sure about that last part
what formula did you use
viral abyss
what formula did you use
its not a formula?
viral abyss
show your calculations
180-102=78 78x2=156
tulip spear
180-102=78 78x2=156
it's not an inscribed angle
viral abyss
it's not an inscribed angle
ok now what
tulip spear
ok now what
so there is a theorem/formula for this
viral abyss
so there is a theorem/formula for this
ok
viral abyss
2*(180-102)=95+y
61
tulip spear
and what is the threoem claled?
"intersecting secants theorem"
viral abyss
"intersecting secants theorem"
hep this one 
still marlin
Then if you add the angle with value x to that angle you have supplementary angles
viral abyss
tulip spear
hep this one <:Worlds_Peepo_Pray:813957323503697920>
just do the supplementary thing again lol
2(180-x)=30+(2x-30)
viral abyss
2(180-x)=30+(2x-30)
is there a reason why you always multiply the angle in the circle - 180 then times 2?
tulip spear
is there a reason why you always multiply the angle in the circle - 180 then tim...
to get the form that the theorem states
calm coralBOT
@viral abyss Has your question been resolved?
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lost arch
hello i need help
calm coralBOT
hello i need help
velvet osprey
lost arch
hey u there?
grim blade
part i got upto
you can now use the formula Area = ab sin C /2
lost arch
how
grim blade
alternatively, if you’re not allowed to use it, you can calculate a height of the triangle and then use Area = bh/2
lost arch
i dont have 2 sides
grim blade
alternatively, if you’re not allowed to use it, you can calculate a height of th...
using trig ratios
grim blade
i dont have 2 sides
Do you know the Sine Law?
velvet osprey
calculate any other side of ABD
lost arch
i only have all the sides for triangle cdb
grim blade
you mean angles?
lost arch
yes
velvet osprey
i only have all the sides for triangle cdb
you have one side and all three angles in BCD
lost arch
angle
lost arch
you have one side and all three angles in BCD
yes
lost arch
wht do i do with it
velvet osprey
or really just one would already be enough
velvet osprey
you can now use the formula Area = ab sin C /2
.
mighty maple
Yoo can someone help me to do some Calculation please
grim blade
Yoo can someone help me to do some Calculation please
Please use another help channel, like #help-27 ; this one is occupied
mighty maple
Please use another help channel, like <#903486480075354182> ; this one is occupi...
Oh ok
lost arch
i did x= 5.6/sin34 times sin121
which gave me 8.6
then i did 0.5 x 8.6 x 5.6 x sin25
i got 10.17
lost arch
Please use another help channel, like <#903486480075354182> ; this one is occupi...
is that it?
grim blade
which gave me 8.6
so that’s BC then
lost arch
then i did 0.5 x 8.6 x 5.6 x sin25
like this
grim blade
then i did 0.5 x 8.6 x 5.6 x sin25
oh you’re supposed to use the angle between the sides, so it’s wrong
lost arch
wdm
grim blade
it should be sin 121
lost arch
so .5 x 8.6 x 6.6 x sin121?
grim blade
oh whoops I read it wrong
grim blade
then i did 0.5 x 8.6 x 5.6 x sin25
this should be right
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Available help channel!
grave storm
i need help on my ixl
calm coralBOT
i need help on my ixl
vernal cedar
uh what do u need ?
grave storm
my ixl
vernal cedar
idk what ixl mean
velvet osprey
do you know how to plot points on a coordinate grid generally
grave storm
yes
velvet osprey
ok then what's troubling you here
grave storm
how to plot and what nuber goes first
velvet osprey
x coordinate always comes first
calm coralBOT
@grave storm Has your question been resolved?
wet remnant
Help
wet remnant
like the possible routes
grim blade
yes
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quaint sapphire
calm coralBOT
dull wagon
yes
quaint sapphire
i did that and got
velvet osprey
do you know how to proceed in general when finding the min or max value of a function
calm coralBOT
@quaint sapphire Has your question been resolved?
sour needle
Yeah and now solve that equation.
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humble zealot
hello, if we have two groups G and H, and L is a subgroup of G x H, then is it true that L must be of the form L = G' x H', where G' and H' are subgroups of G and H respectively?
humble zealot
i'm asked to draw the subgroup lattices of these and i dont know if there's a "rule" on how to find subgroups of direct products
elder pawn
$\brc{(g,g):g\in G}$ is a subgroup of $G\times G$ but not the product of subgroups
potent lotusBOT
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calm coralBOT
@humble zealot Has your question been resolved?
calm coralBOT
@humble zealot Has your question been resolved?
stable trellis
For:
x ≠ -c, Solve:
x^2 - ax + cx - bx - ac - bc = 0
calm coralBOT
For:
x ≠ -c, Solve:
x^2 - ax + cx - bx - ac - bc = 0
tulip spear
For:
x ≠ -c, Solve:
x^2 - ax + cx - bx - ac - bc = 0
tried quad formula/factorization?
wraith geode
For:
x ≠ -c, Solve:
x^2 - ax + cx - bx - ac - bc = 0
I'm guessing you'd first simplify this to make it a proper quadratic equation, then start from there
stable trellis
I did with quad formula but i want to do it with factorization
tulip spear
I did with quad formula but i want to do it with factorization
it turned into a rational solution or irrational?
if rational we can factor it
if not we cant
stable trellis
it turned into a rational solution or irrational?
It wasnt with numbers
So we prob can factorise it
tulip spear
It wasnt with numbers
what?
tulip spear
did any of the letters have a root under them in the final answer or no
stable trellis
No
tulip spear
ok then its factorable
stable trellis
Yeah but how do i do that
tulip spear
For:
x ≠ -c, Solve:
x^2 - ax + cx - bx - ac - bc = 0
group the x-terms and constant terms first
tulip spear
Yeah but how do i do that
getting there!
stable trellis
Ok so x^2 + x(a + c - b) -c(a + b)
tulip spear
hint: ||get a form with (x+c) in all of the terms||
tulip spear
Ok so x^2 + x(a + c - b) -c(a + b)
yeah i will backtrack
tulip spear
hint: ||get a form with (x+c) in all of the terms||
this is the way i think
since x=-c is a root
stable trellis
But we need to find the other one
stable trellis
hint: ||get a form with (x+c) in all of the terms||
How am i supposed to do that
tulip spear
How am i supposed to do that
there is a c in at least one term of every "grouping"
pair the c's up with each other
random escarp
Maybe x² +x(-a + c -b) -c(a + b) = 0
stable trellis
there is a c in at least one term of every "grouping"
Not in x^2 though
tulip spear
trust me bro im cooking
wraith geode
If you rearrange the terms you'll see a pattern easier, using which you can group them:
x^2 - ax + cx - bx - ac - bc = 0
x^2 - ax - bx + cx - ac - bc = 0 (Rearranged)
||x(x - a - b) + c(x - a - b) = 0||
||(x + c)(x - a - b) = 0||
tulip spear
If you rearrange the terms you'll see a pattern easier, using which you can grou...
bro just cannot hold it in 😭
what is hard about guiding
wraith geode
I told him to rearrage + I responsibly hid the solution.
Just trying my best to explain
tulip spear
Not in x^2 though
well, you will see once you group it
stable trellis
If you rearrange the terms you'll see a pattern easier, using which you can grou...
Ohhhh
tulip spear
in a sense, "match" the terms containing b, c, and the lone x^2 term with the cx term (this produces (x+c) regardless)
tulip spear
Just trying my best to explain
i don't see no "explaining"
i see a sentence we already covered and full math after that
no words
wraith geode
Ok man
stable trellis
well he decided to drop the full sol ig
Ahaha dw
I prob have other equations
In my hw
Lemme check
tulip spear
k
stable trellis
nah i dont
I did the rest of them
Im proud of myself
Do i close this now?
.close
marsh blade
calm coralBOT
marsh blade
how can I know horizontal translations
i usually look at point 0,1
but this graph is harde
pure kayak
translation from what exactly
pure kayak
could you put some brackets in there please
red umbra
when u put x=0
red umbra
i wanna find a^x-h
is is a^x - h
if u check for x=0 a is 1 right?
so 1-h should be 2
ohhh
marsh blade
hm
marsh blade
yes
marsh blade
@pure kayak
red umbra
so u dont know neither a nor h