v^2/a_perpendicular, usually defined for projectiles (a_perpendicular is a perpendicular to the velocity)
#help-19
toxic rose
turbid comet
Let us take u= mgsin@ - bv
honest ore
alr
turbid comet
v^2/a_perpendicular, usually defined for projectiles (a_perpendicular is a perpe...
But won't we need the distance from the point of banking
That is what we were taught
honest ore
r = 100 worked anyways
toxic rose
i am not sure I haven't read the question this is a really long thread 
turbid comet
Let us take u= mgsin@ - bv
We assume this substitution
Now we have a simpler integral but that is not it
Our differential operator is still dv
And we need it to be du
We know du/dv = -b
Now we substitute the value of dv in the integral to get
@honest ore are all these steps clear
turbid comet
Our integral looks something like this
honest ore
We know du/dv = -b
so this means dv = du/-b
turbid comet
But the denominator is slightly complicated
turbid comet
so this means dv = du/-b
Yes
honest ore
and the original was dv/u
turbid comet
so this means dv = du/-b
I didn't give any context on how this came
turbid comet
and the original was dv/u
Yes
honest ore
ok i kinda get it
theres a curve on the test anyways so i just need to get most of it
whats the next step btw
honest ore
alr
honest ore
I didn't give any context on how this came
actually can i get context on this
turbid comet
actually can i get context on this
u = mgsin¥ - bv
Now we differentiate it wrt v
To get du/dv = -b
turbid comet
?
honest ore
or is wrt v short for something
turbid comet
With respect to
turbid comet
Alright the next question ?
honest ore
what comes next
turbid comet
This one is pretty much done from here
turbid comet
what comes next
We have ln(mgsin@ - bv) = -(C+t)m/b
honest ore
yeah idk how u got there
turbid comet
We had integral du/-bu = mt right
Now after integrating the left side we get
(-1/b)*(lnu)
Where we substitute the value of u
To get ln(mgsin@ - bv) = -mt/u + C
honest ore
wait when did the left side become -mt/u + C
honest ore
yeah thats a good idea i think
turbid comet
I am really sorry while typing i messed it up
It was supposed to be tb/m
@honest ore
honest ore
u mean -tb/m
turbid comet
Yes
honest ore
<@&286206848099549185>
honest ore
im gonna hope the reflection isnt hiding anything important
turbid comet
It isn't
honest ore
.close
odd edgeBOT
turbid comet
?
deep flicker
vernal yacht
This channel has been closed
brittle plinth
please open a new channel and repost the question
vernal yacht
Consider claiming a new one
odd edgeBOT
Available help channel!
bronze citrus
Sup
short terrace
,rccw
clever fjordBOT
short terrace
bronze citrus
Is the formula $\frac{1}{Req} = \frac{1}{R}+ \frac{1}{R} +\frac{1}{2R}$
clever fjordBOT
Ryne___np
ember pelican
Ryne\_\_\_np
that is for resistors in paraellel
wooden python
btw $R_{eq}$
clever fjordBOT
Ann
wooden python
also yeah these guys of yours are in series
bronze citrus
that is for resistors in paraellel
Oh so in this case they are not?
ember pelican
also yeah these guys of yours are in series
.
bronze citrus
So the sum is 4R
ember pelican
So the sum is 4R
you would just add thme up
odd edgeBOT
lilac lichen
Ryne\_\_\_np
is this parallel
bronze citrus
is this parallel
They said in series
I thought they were parallel because of the node
Like that
But im wrong
odd edgeBOT
Available help channel!
fleet lake
odd edgeBOT
pastel steeple
,rccw
clever fjordBOT
pastel steeple
ugh
fleet lake
,rccw
fleet lake
rccw
fleet lake
,rccw
clever fjordBOT
pastel steeple
💀 ok
fleet lake
Cos and sin here must be opposite in sign yet equal in magnitude
keen spade
Cos and sin here must be opposite in sign yet equal in magnitude
What did you do in this question
What your attempt/thought process
fleet lake
Either Cos or sin here must be -ve here having same magnitude
keen spade
Convert tan into sin/cos
Then take LCM you get an identity
fleet lake
Tan an odd function will remove - out
fleet lake
Convert tan into sin/cos
Then take LCM you get an identity
Ohk
Ty I'll try after supper
.close
odd edgeBOT
odd edgeBOT
Available help channel!
solar tapir
how big is this number?
odd edgeBOT
how big is this number?
solar tapir
and how would i calculate it myself?
solar tapir
e7.625e6
leaden karma
It’s 10^(7.625 * 10^6)
solar tapir
damn
mystic nova
you're gonna break the bot
solar tapir
is it that big?
clever fjordBOT
mystic nova
stoic cloud
Yeah it didn’t compute…
stoic cloud
well it
devout hedge
balatro numbers are that big.
stoic cloud
*it’s a umber with 7,625,000 digits
solar tapir
at 45m calculations
stoic cloud
Cuz you have 10⁷⁶²⁵⁰⁰⁰
solar tapir
balatro numbers *are* that big.
doesnt help that im using a mod that needs its own system for the numbers
solar tapir
*it’s a umber with 7,625,000 digits
DAMN
stoic cloud
this is balatro?
solar tapir
yes
stoic cloud
never played it 
I should tho
solar tapir
modded tho
stoic cloud
solar tapir
hope my laptop doesnt die
stoic cloud
same here lmao
strange aspen
I love balatro 🔥🔥🔥🔥
devout hedge
you have a thousand jokers... probably you're going to be there for 2 hours.
but do you still have a question?
strange aspen
1557 jokers ?????!
shell haven
Bro I think that's more than the world's GDP man😭
solar tapir
Bro I think that's more than the world's GDP man😭
more than atoms in the universe
stoic cloud
Dude i feel like the odd one out not knowing what yall are tallking about 
solar tapir
doesn't look like it, ma'am...
there is a /
shell haven
Dude i feel like the odd one out not knowing what yall are tallking about <:sad:...
Balatro funny card game and big number is all I know
solar tapir
anyway, any other math questions?
not rn
stoic cloud
devout hedge
alright.
odd edgeBOT
If you are done with this channel, please mark your problem as solved by typing .close
@solar tapir Has your question been resolved?
Available help channel!
lime merlin
hi
lime merlin
can anyone help?
merry finch
Post your question!
lime merlin
can you explain how to do this?
quasi sparrow
can you explain how to do this?
can you show the formula for Newton Quotient you were taught
lime merlin
can you show the formula for Newton Quotient you were taught
f(x+h)-f(x)/h
lime merlin
not rlly. im trying to understand it
quasi sparrow
y(x+h) is the function y(x) except where you replace x+h wherever there is an x
waxen talon
can you explain how to do this?
consolas
waxen talon
font name
quasi sparrow
i aint understanding any of this. im going back to the textbook
do a simpler example first
if g(x) = x^3. do you know what g(x+h) equals?
odd edgeBOT
@lime merlin Has your question been resolved?
jolly wraith
Hello, I'm currently working with some patological cases of l'hopital's rule. And I don't know how I should describe numerator and denominator. For numerator, what becomes x^2*sin(1/x)? Since it becomes 0 x undefined I don't know how to describe it
jolly wraith
wooden python
are you REQUIRED to do it with l'hop
also whoever TeX'd this should learn that \sin exists.
jolly wraith
I'm the one who did that sorry haha
wooden python
$\lim_{x \to 0} \frac{x^2 \sin(1/x)}{\sin(x)}$
clever fjordBOT
Ann
wooden python
anyway again, are you required to do this with l'hop?
jolly wraith
But yes I'm required to do it with l'hop and show that there's no answer. And I have to do it again with numerator and denominator changed, and show that it works.
wooden python
uhhh
i mean like, $\lim_{x \to 0} x^2 \sin(1/x) = 0$ by e.g. squeeze theorem, so LH is \textit{applicable}.
clever fjordBOT
Ann
wooden python
and then there's some run-around when it comes to taking the derivatives of top and bottom and staring long & hard at the resulting limit
with the ultimate conclusion being that l'hop doesn't give us anything useful
jolly wraith
I'm forced to solve it with l'hop for this equation, and I don't really know how I should interprete 0 muliplied by sin(infinity), like the numerator
Is it undefined?
jolly wraith
Yes, that's in the syllabus and it's the part of training, according to professor
wooden python
0*sin(∞) as-written is undefined, but this simply means you have to resort to some other means to find the limit of x^2 sin(1/x).
so by the looks of it, you've just explicitly had all means of solving this limit taken away from you
💔
and you're simply unable to do it because of red tape.
and bureaucracy.
jolly wraith
So I can't go further with l'hop rule in this equation?
odd edgeBOT
trim dome
0*sin(∞) as-written is undefined, but this simply means you have to resort to so...
wasnt there this one theorem where if you have lim_{x -> 0} f(x)g(x) and g(x) is bounded and lim_{x -> 0} f(x) = 0 then lim_{x -> 0} f(x)g(x) = 0??
or am i remembering wrong
wooden python
and by the looks of it OP is barred from using that
trim dome
ohhh shi i see
trim dome
and by the looks of it OP is barred from using that
cant you say numerator lim_{x->0} sin(1/x)/(1/x^2) and LH that?
oh you still get cos(1/x) dont you
mb
odd edgeBOT
Available help channel!
native marten
hey guys I need some help.
lim x->1 (x^x -1)/(1-xln(x))
Do I need to check left hand side and right hand side with the limit? Why/why not?
wooden python
$\lim_{x \to 1} \frac{x^x - 1}{1 - x\ln(x)}$
clever fjordBOT
Ann
native marten
ln(1) = 0, so -1 * 0 = 0
wooden python
yeah so your denominator approaches 1 doesnt it
native marten
yeah so your denominator approaches 1 doesnt it
hold on my bad, the denominator should be 1-x+ln(x), not 1-xln(x). my bad!
please excuse, my brain is fried :(
wooden python
ah that changes things doesnt it
native marten
it does x)
odd edgeBOT
@native marten Has your question been resolved?
wooden python
right so then for $\lim_{x \to 1} \frac{e^{x \ln(x)} - 1}{1 - x + \ln(x)}$...
clever fjordBOT
Ann
wooden python
i dont yet see a pressing need to consider two sides separately
fluid bluff
huh
native marten
well when x->1, we get 1-1 = 0 on the top, and 1-1=0 in the bottom. We then apply lhospital and get ln(x) + 1 on the top and -1 + 1/x on the bottom
wooden python
that's the derivative of just x ln(x)
not e^(x ln(x))
well, i suppose if you replace e^(x ln(x)) - 1 with its asymptotic equivalent then yes this is what you get
native marten
oh ure right my bad
hmm lemme try again
so the top should be exp(xln(x))*(ln(x)+1)
this is what I have then
odd edgeBOT
@native marten Has your question been resolved?
odd edgeBOT
@native marten Has your question been resolved?
orchid torrent
This is fine so far
now notice that the numerator approaches 1 while the denominator approaches 0
what does that tell you
native marten
what does that tell you
not so sure tbh
we cant insert 1 into the denominator as then we would divide by 0
orchid torrent
not so sure tbh
This should be reminding you of a general idea
when you get a result of a/0 (where a is nonzero) after direct substitution, what does that mean
native marten
we approach the 1 from left and right?
orchid torrent
that's what the $\lim_{x \to 1}$ is saying - you need to consider both left and right hand limits
clever fjordBOT
Civil Service Pigeon
orchid torrent
that is not what I'm asking
native marten
hmm then i dont know
native marten
no
orchid torrent
mhm
now consider 2/0.1, 2/0.01, 2/0.001, ...
what do you notice about these quotients
native marten
they get smaller?
orchid torrent
they get smaller?
you sure?
native marten
I mean 2/somethign smaller and smaller gets bigger, because the denominator gets smaller
orchid torrent
the quotients get bigger
in fact, they tend towards infinity
but here, the denominators are approaching zero from the right
but we can also have the denominators approach zero from the left
aka 2/-0.1, 2/-0.01, 2/-0.001, etc
what do we approach in this case
alright bye ig
native marten
minus infinity i think
sorry I had to leave the computer for a sec
so then we get infty and -infty, which means our thing diverges
orchid torrent
so then we get infty and -infty, which means our thing diverges
yes
the division by zero means you approach +infty from one side and -infty from the other
hence does not exist
orchid torrent
when you get a result of a/0 (where a is nonzero) after direct substitution, wha...
the idea here is that you're approaching +infty or -infty
native marten
okay. And we are approaching from left and right each because x approaches 1, which we cannot put into the denominator directly, therefore we need to approach from left and right each
orchid torrent
the denominator approaches zero from different direction as x approaches 1 from different sides
if that's what you're going for
last jetty
I keep getting atan(-1) idk what im doing wrong
odd edgeBOT
I keep getting atan(-1) idk what im doing wrong
last jetty
especially considering this problem is really simple
quasi sparrow
maybe try inputing an exact angle instead of relying on a function
last jetty
perhaps
forest sky
your problem is that (-2,2) is in the second quadrant but arctan always returns angles in the first and fourth quadrants
last jetty
your problem is that (-2,2) is in the second quadrant but arctan always returns ...
oh I forgot about that
so -atan(-1)?
wait no
wait yes
no
forest sky
remember than tan is pi-periodic
wet apex
i would advise you learn the curves for sin, cos, and tan
last jetty
I swear im usually smarter than this I just stayed up late finishing a group project my friends forgot about so im currently trying to do calc III off 3 hours of sleep
wet apex
fr example suppose we imagine the tan function we know it diverges at $-\pi / 2$ and $\pi / 2$
clever fjordBOT
ben
wet apex
and now we can invert this
forest sky
yes
wet apex
yes
last jetty
o
forest sky
uh why did it turn from pi into pi/2
last jetty
.close
odd edgeBOT
last jetty
uh why did it turn from pi into pi/2
idk 3 hours of sleep does things to brain I meant pi
.close
odd edgeBOT
Available help channel!
manic grail
is piecewise continuity mentioned so that the Reimann integral is defined?
manic grail
yes
in the Reimann integral
i remember it was mentioned in a different way
it was something like a finite amount of discontinious points or something like that
does piecewise continuity cover like the least condition
low locust
not quite the same but close enough
leaden karma
All sorts of weird functions are integrable
manic grail
All sorts of weird functions are integrable
is there a case where a function can be written as this
but isnt piecewise continious
wet apex
define the space
manic grail
yea well cant we have a case where it is integrable
but it doesnt satisfy piecewise continuity
forest sky
(although pretty much every function you work with in practice will meet this condition)
leaden karma
Yes you can
low locust
there are lots of weird functions which are far from continuous but integrable
manic grail
Yes you can
then why havent we defined laplace transformation in that case
wet apex
literally untrue @wierd greek name
manic grail
is this not the general definition of laplace transformation?
forest sky
you can define the laplace transform for all integrable functions (depending on what integral you even use!). but for an ode course you don't need to get deep into the weeds of what functions can be laplace transformed if they won't appear anyway
manic grail
you can define the laplace transform for all integrable functions (depending on ...
oh ok
so this isnt the general definition
leaden karma
then why havent we defined laplace transformation in that case
Because those functions are edge cases and will almost surely never come up in any practical context
forest sky
yes, it's general enough for the purposes of the course. the same integral always applies, just a matter of when it's defined which they don't want to get into
wet apex
why dont you provide a theorem instead of something something somebody says
low locust
your fellow students will certainly prefer such a definition compared to defining it on some weird function space which they dont understand
say as a lebesgue integral with respect to some other measure and whatnot
wet apex
so everyone can be precise
manic grail
your fellow students will certainly prefer such a definition compared to definin...
yea i understand why they make it simpler
im just here to understand whats true
manic grail
say as a lebesgue integral with respect to some other measure and whatnot
idk the lebesgue integral
low locust
well take an analysis book and 1-2 months
manic grail
hasnt come up yet atleast
wet apex
okay so you do not know any measure theory
low locust
have fun
quasi sparrow
idk the lebesgue integral
then piecewise continuous is enough and move on
wet apex
and so do some people in chat
manic grail
well take an analysis book and 1-2 months
i mean i did some stuff
but like idk what lebesgue integral is inside
like what course
and what i need for it or where to start
wet apex
can we close this section
manic grail
can we close this section
there are plenty of other channels if you need to chat about something else
manic grail
developing the lebesgue integral genuinely takes weeks
what is it in
like when should i learn it
and in what context
manic grail
wdym i wont need it
manic grail
you arent studying proper math
i am
leaden karma
Uhm
low locust
are you sure
manic grail
this is the only reason im studying math
wet apex
i just mean if you close this one and a start a new one you'll get fresh eyes
low locust
ben just buzz off
wet apex
my purpose and role is not to discourage math
manic grail
but yea i just study math rn without being in uni for the purpose of studying math
but idk in which order to study stuff
what should i do after differential equations
quasi sparrow
well take an analysis book and 1-2 months
dena told you here
leaden karma
The laplace transform is defined in the easiest and simplest way possible because that’s all you need for 99.99999% of cases
manic grail
i have completed calc 1,2 i am in middle of calc 3 and im finishing differntial equations probably in the next 2 weeks
low locust
literally just pick up any RA textbook and work through it
manic grail
should i finish calc 3 first?
idk if i should already know the lesbugue integral you said
or im doing something in wrong order
low locust
this whole system with doing calc without analysis is weird anyway
quasi sparrow
just follow some university recommendation for bachelors' in math
manic grail
this whole system with doing calc without analysis is weird anyway
i mean i am doing analysis
low locust
you will do the relevant things when you encounter them in the book
you are doing calc
low locust
well then pick up a fucking book
manic grail
but idk where to find a well documented in order course
low locust
there are a million analysis textbooks
low locust
lots
quasi sparrow
low locust
legally is a different question probably
manic grail
legally is a different question probably
send me one
low locust
no
quasi sparrow
low locust
idc
manic grail
also is the content of real analysis same for every book or does it differ
low locust
you can if you want to
manic grail
idc
yea well im just asking what youd think is best
i could either complete calc 3 from pauls notes and excersices
since i have it in order and then find a source or do at the same time
low locust
well I mean every RA book will talk about convergence, continuity, differentiability, integrals etc
in that order
the level of detail etc will of course vary
low locust
analysis is calc but done properly
leaden karma
Real analysis is just rigorous calculus
manic grail
well like for every proof or question i have i always end up on some real analysis thing
i have noticed that
i try to do all proofs of everything i find in calc as in theorems and it is always found in some real analysis context source
manic grail
but i thought there were more complex stuff outside of convergence integrals etc i thought it was completely different just part of it had proofs
low locust
basically
manic grail
damn
so instead of doing calc and for every theorem searching for proof out of that source it would be the same if i did RA
then whats the point of calc courses if RA is redoing it again properly
low locust
not all students need proofs
manic grail
damn i feel stupid now
what i have been doing is following a calc course and searching outside it for proofs for everything
low locust
and it helps when you can focus on the proofs in analysis because you know the general stuff about functions and derivatives etc already
manic grail
when i could have just done RA
@low locust why can you not send a free book link on RA?
leaden karma
It’s better if you do calc before RA, because it’s easier to prove things when you already know how they work
low locust
because maybe you could put some fucking effort into this?
manic grail
because maybe you could put some fucking effort into this?
but how will i know if the book is good
low locust
look at reviews
manic grail
https://discord.com/channels/268882317391429632/903463355619110912/1420157034224...
are those free?
leaden karma
Bro
manic grail
oh wait you mean like actual published book
quasi sparrow
putting in so much effort
low locust
do we have to spoonfeed everything to you?
signal yacht
oh wait you mean like actual published book
?
quasi sparrow
maybe recommending real analysis isn't a good idea dena
manic grail
well that would prob not be free
signal yacht
maybe recommending real analysis isn't a good idea dena
yeah maybe not
probably not
low locust
maybe recommending real analysis isn't a good idea dena
well he wants to learn it ¯_(ツ)_/¯
manic grail
maybe recommending real analysis isn't a good idea dena
why is it not
and if it isnt what is
manic grail
real analysis requires effort
i am putting effort
quasi sparrow
because maybe you could put some fucking effort into this?
^
signal yacht
pick up like spivak
manic grail
but like for example
signal yacht
there you go
manic grail
i found pauls notes
signal yacht
pick up spivak
manic grail
and after i went half way yall said its bad
low locust
have you in the past 15 minutes googled for RA textbooks
quasi sparrow
damn dena
why are you asking such hard questions
what is this a real analysis course?
manic grail
have you in the past 15 minutes googled for RA textbooks
i found some but i havent searched somewhere to find them for free
low locust
well certain sites will have them
manic grail
pick up like spivak
ok ill check it out
signal yacht
it's called calculus but it's analysis.
low locust
btw literally first link is a pdf
signal yacht
show me a screenshot or smth blud
signal yacht
yes.
manic grail
these are considered RA?
manic grail
ok so this covers all of what we call Real analysis ?
low locust
you absolutely need to be familiar with basics like those
manic grail
it may very book to book but its good for like as in what math students get taught
in the RA course
right?
signal yacht
...what
its an analysis text yes.
if you consider yourself proficient with basic material, you're not obliged to do it
manic grail
idk sorry when i hear of Real analysis it sounds more of a way to view math than a course like calc
manic grail
if you consider yourself proficient with basic material, you're not obliged to d...
no i will do it i think i will have gaps in proofs and stuff like that
wow so this just goes over proofs for even very basic stuff
signal yacht
wow so this just goes over proofs for even very basic stuff
well
it's an analysis text
manic grail
if you say so
nice thank you @signal yacht appreciate it
does this include any complex stuff aswell?
complex numbers
low locust
can you like read the contents of the book?
all books include a table of contents at the beginning
signal yacht
stick to freaking spivak
manic grail
manic grail
stick to freaking spivak
are they not good?
low locust
rudin is also good
signal yacht
baby rudin is
low locust
just pick a book
green elm
real and complex analysis is about two courses more advanced than what you're studying, it's apples to oranges
manic grail
but is Mathematicl analysis something else?
low locust
you could google for reviews about those books
signal yacht
but is Mathematicl analysis something else?
no.
manic grail
ok so these 2 are covering the same stuff
low locust
but both spivak and rudin are names commonly thrown around when talking about good books
manic grail
this red one seems good documented and has good reviews
is the mathematical analysis one a combination of RA and CA?
low locust
how about you read the table of contents
manic grail
the mathematical analysis one seems more complicated
manic grail
it starts with topology stuff
the other one says abstract integratino
but idk what most of what im reading mean
signal yacht
consider googling
manic grail
consider googling
well yea but the names arent gonna tell me much
if you had to put them in order
signal yacht
what?
manic grail
which of those 2 starts earlier on
like topology
in math unis
is many semesters later than RA
so is the mathematical analysis one much more advanced than the other
signal yacht
……so topology is not analysis
manic grail
……so topology is not analysis
idk what it is i just saw it inside the mathematical analysis book
signal yacht
did you
signal yacht
well
manic grail
the other like this
manic grail
from my perspective the second one is closer to calculus and atleast where i am now
low locust
this one is way too advanced for you
manic grail
from the description the first one feels like i need a lot more knowledge to even start
low locust
like bungo said
low locust
take this or spivak
signal yacht
baby rudin or spivak
manic grail
this is simpler?
manic grail
whats that mean
signal yacht
pick up principles of mathematical analysis
signal yacht
manic grail
idk if its a RA text book or something else
i mean im confused on what RA is at this point so many different titles but ill start this
since the other is more advance
do i need to do something else before starting it
in your opinion
signal yacht
analysis is calculus but not handwavy
manic grail
or does it start with basics
manic grail
tbh i just got scared because it mentioned topology
manic grail
https://david92jackson.neocities.org/images/Principles_of_Mathematical_Analysis-Rudin.pdf this a correct pdf for it i think
signal yacht
i dunno
manic grail
doesnt have the wallpaper
signal yacht
if it works it works
manic grail
if it works it works
yea ig
but like here it says some about complex analyiss
idk if its wrong book or it just has also complex analyiss
cause you said its RA book
signal yacht
pretty sure thats not a part of the book
its promotion material for the publisher
have you never touched a book before? /gen
signal yacht
well
considering that the book is authored by rudin not rudin et al
and the list literally has 'principles of mathematical analysis' in there
no.
manic grail
it says in preface that this is for first year math students
is RA not 5th semester?
or later
manic grail
before calc 2/3 ?
low locust
I didnt have calc courses
signal yacht
before calc 2/3 ?
calc 2 and 3 are in highschool
manic grail
the ones i found from are 8 semesters
low locust
3 years. normal bachelor
manic grail
i dont think series are done in highschool
low locust
oh yeah I suppose technically I had calc content in hs
manic grail
at least i was taught calc 2 material in hs
well you get taught integration technicks
but not all of calc 2
low locust
but definitely not a dedicated calc course in university
signal yacht
theres multi variable calculus in unis here
or math 1
which begins with calc 3
and then goes into analysis territory
manic grail
where are you from
signal yacht
india
signal yacht
eh
kinda
not very well
not ideas of convergence actually
so ig half of calc 2 then
manic grail
3 years. normal bachelor
ah ok here its 4 years
so you got introduced to basic topology and lesbugue theory and all these in first year?
low locust
yes
just forget that this chapter in the book is called the scary word topology
its just about open and closed sets and stuff
its really not that crazy
manic grail
how can it have like at the middle of the book differntiation and continuity isnt that something ive already done
manic grail
like mean value theorem is high school material
manic grail
LMVT is what
oh mean value theorem
yea so because it is continious in [a,b]
it has maximum and minimum
low locust
prove that
manic grail
ok
low locust
and that will rely on some other lemma etc
thats the things you do in RA
prove the things you take for granted in calc
manic grail
prove that
i have done that already
low locust
well then you are in luck and can go over the relevant pages in the book quicker
signal yacht
we just go 'well it makes sense innit'
manic grail
what does IVT stand for
low locust
this is not a sign to skip the book
manic grail
this is not a sign to skip the book
oh ok
signal yacht
intermediate value theorem.
manic grail
idk the english names fr
low locust
just because you proved some theorems from it
manic grail
Using bolzano theorem
low locust
you had bolzano theorem in high school?
manic grail
yes
low locust
weird
well the earlier chapters in the book will go by quicker then
but dont skip them
manic grail
this was my highschool book
it mentions ε,δ defintions too
but arent used in proofs
manic grail
wdym
low locust
?????
low locust
analysis without epsilons isnt analysis
manic grail
analysis without epsilons isnt analysis
i didnt say its RA
but it doesnt have proof for bolzanos theorem
manic grail
then some theorems for f'>0 f increasing etc
curvature
or whatever we call it in english
Fermat theorem
with proof
by δ definition
@low locust is LMVT supposed to not be before calc 2?
low locust
I dont fucking care if you do it before or after
manic grail
i have done it
low locust
good for you
low locust
it doesnt matter
quasi sparrow
I dont fucking care if you do it before or after
time to read #「helpers-lounge」 message
manic grail
also rolle is proven by fermat theorem
someone asked before
f'(xm) = 0 and f'(xM) = 0
i have seen the Reimann integral with RA and so have i for the properties proofs
thats why i was thinking of starting this
low locust
are you even listening to us
manic grail
are you even listening to us
isnt this just a Real analysis textbook
so how will it be any different if im still studying the same course
low locust
3 people have told you the book is too advanced for you
manic grail
yea but then yall said idk how to prove LMVT and stuff like that
but ive done that already
like the differentiation and integration proofs a lot i have done
i had some text book irl it was covering big part of those
manic grail
wdym
manic grail
well then go and have fun
does this book not explain everything fully for someone to understand
you said real analysis is just calc but with proofs
like half of this book i have already seen the mathematical analysis one
ill just take this slowly ig
.close
odd edgeBOT
odd edgeBOT
Available help channel!
lone elbow
what is the implicit function theorem?
odd edgeBOT
thin geyser
When you have a function from R^n to R^m where n > m, the IFT gives you, under a mild condition, the existence of a differentiable function g from R^(n-m) to R^m such that the graph of g are locally the roots of f.
It is mainly helpful to establish that such a g exists, even when you can't write it down explicitly, and that this g is differentiable
odd edgeBOT
Available help channel!
mild hemlock
I need help solving/getting the hang of this
odd edgeBOT
I need help solving/getting the hang of this
mild hemlock
during class, i follow through and answer all right but then when im on my own i kinda get stumped
mild hemlock
wdym
green elm
x^2 - 81 = 0 is the same as x^2 = what?
mild hemlock
idk :/
should i take a break? ive been doing alot of hw, i cant think without my head hurting
mild hemlock
x^2 - 81 = 0 is the same as x^2 = what?
i obviously know what this is but its not clicking for me rn 😭
sturdy cape
-# (well it could help if you could say what you know it to be; else Bungo can't tell whether it does click for you)
green elm
if you have something of the form
a - b = 0
that's the same as
a = b
(just add b to each side)
can you apply that to x^2 - 81 = 0?
mild hemlock
81?
sturdy cape
x^2 - 81 = 0 is the same as x^2 = what?
@green elm I believe that's in response to your message here
-# It's right btw @mild hemlock
mild hemlock
are there any others?
like factors?
green elm
any other value for x such that x^2 = 81?
mild hemlock
any other value for x such that x^2 = 81?
i cant think of any other
green elm
hint: are there any negative solutions?
solar galleon
i cant think of any other
Have u got the answer/
mild hemlock
hint: are there any negative solutions?
oh yeah!! i forgot
-9
because its -81 not +81
green elm
no...
x^2 = 81
not -81
but both x = 9 and x = -9 satisfy that equation
because (-9) squared is +81
(recall that negative times negative = positive)
solar galleon
oh wait it was just asking for x=
how to u make the equation equal to 0?
mild hemlock
subtract both sides?
mild hemlock
or add* to make it 0
solar galleon
yep
solar galleon
or add* to make it 0
and then you do the factorization
mild hemlock
ill brb
odd edgeBOT
@mild hemlock Has your question been resolved?
dusk moon
I'm confused on how to go about these questions. I already found Nullspace of identity matrix but I'm having trouble finding range
tacit elm
Start with the null space
tacit elm
I'm confused on how to go about these questions. I already found Nullspace of id...
Can you tell me what is the null space of the identity matrix ?
dusk moon
N(I_n) ={x:x=0}
tacit elm
So what’s the dimension of the nullity ?
dusk moon
That's not a topic I've seen yet I've only seen range and Nullspace so far
tacit elm
You haven’t seen the range nullity theorem ?
dusk moon
No
tacit elm
Ok so let’s think of the range then. Take a random vector y, can you find a vector x such as Ix = y ?
dusk moon
it would just be x =y
tacit elm
Good so what does that mean for range ?
dusk moon
well I know definition is R(A) ={y: Ax=y} , y is like output I think
tacit elm
Yes basically, it means all the vectors that A can « reach »
So the fact that for any vector y, you find x such as Ix = y
What does it mean for range I
tacit elm
well I know definition is R(A) ={y: Ax=y} , y is like output I think
Meow ?
dusk moon
I'm not sure if I understand what you mean
tacit elm
Ok so you define the range of A as all the vectors y that can be written as Ax right ?
dusk moon
This is the definition I've been using
tacit elm
Ok
So we just proved that for I. Any vector y can be written as Iy. So any vector y that you choose belongs to R(I)
So R(I) is the whole space
It’s R^n
fringe perch
dawg whut
dusk moon
well for Ax=y x is in R^n And y is in R^m but we are saying Ix=x and y =x so since x is in R^n then y is also in R^n?
tacit elm
well for Ax=y x is in R^n And y is in R^m but we are saying Ix=x and y =x so sin...
You’re talking about R^n -> R^n here.
Because the matrices’ size is nxn
dusk moon
I understand that part but I don't get where the range part is coming from
tacit elm
Can you remove your message ?
So basically, you agree that y is in range A, if you find a vector x such as y = Ax
?
dusk moon
yes
tacit elm
So every possible vector is in range I
Because if you take any possible vector y, then y = I.y
fringe perch
Can you remove your message ?
ma bad
dusk moon
well x=y right can I write R(I_n) ={x: I_n x=x, x in R^n}
tacit elm
Which makes the range of I any possible vector. That means range of y is R^n
Yes, but that’s true for any x
Which makes R(In) = R^n
tacit elm
well x=y right can I write R(I_n) ={x: I_n x=x, x in R^n}
This R(In) that you defined here works for any value of x
dusk moon
but isn't R^n ={x: x=(x_1,....,x_n), where x_1....x_n are real numbers}?
x is a vector here not a coordinate
tacit elm
Yes ? So ?
dusk moon
how does that set equal to the other set if true
tacit elm
x and y are also vectors ! The ones we’ve been talking about
When I say I x = x, x is a vector
dusk moon
I get that
tacit elm
And since this equality works for any x
That means that any x is in range I
So this gives you that R^n (which is any x) is included in R(I)
Which means R^n = R(I)
dusk moon
so x is in the range of I and x is in R^n so range of I =R^n?
I'm trying to see this logically
tacit elm
No I’m saying.
If you take any x in R^n, it also belongs to R(I)
That’s the definition of R^n included in R(I)
Now since R(I) is by definition also part of R^n
That gives you double inclusion : meaning R(I) = R(n)
dusk moon
is R(I) part of R^n because x is part of R^n
tacit elm
is R(I) part of R^n because x is part of R^n
No
R(I) is a subspace of R^n. That MUST be in your course !
Range is part of the coset. Nullity is part of the set
dusk moon
I haven't seen Range of I a subspace of R^n but I have seen proof of Nullspace of a m by n matrix is a subspace of R^n
tacit elm
It’s just by definition
A vector of the range is by definition a vector of the coset that has a preimage
Your teacher sucks. Because he should be more explicit
But he wrote it here
The range is part of R^m (which is your coset here)
dusk moon
By the way this a first course in lin algebra so I'm not familiar with the terms you're speaking about
dusk moon
No, that's the question I'm trying to figure out
tacit elm
Ok, let’s review. By definition, the range is included in R^n, that’s understood right ?
tacit elm
Because the definition of range is all vector y such as Ax = y
So we know that Ax lands in R^n
Because A transforms vectors from R^n to R^n
dusk moon
that's if A =I right
tacit elm
No that’s for any square matrix of size nxn
It takes a vector from Rn as input and gives a vector from Rn as output
dusk moon
in that case I agree
dusk moon
Because the definition of range is all vector y such as Ax = y
Here, is y in range of A ?
tacit elm
Yes !
If you find a vector x such as Ax = y
That’s the very definition of y is in range(A)
To put it very simply the range is all possible outputs
dusk moon
so since if A is n by n and y is in R^n and y is also in range of A then range of A is in R^n?
tacit elm
Range of A is always in R^n
Range of A is all possible outputs of A
Since A is an nxn matrix. Then it’s outputs are in Rn
dusk moon
well assuming if I'm on right track then I understand so far
tacit elm
Ok, so this is not something you need to show everytime
Just understand that range is all possible outputs ok ?
Now what are all possible outputs of I
?
dusk moon
all vectors in R^n
dusk moon
so was it right in front of me this whole time I know Ix=x so it's going from R^n to R^n so all the outputs are from R^n
tacit elm
Yes it is quite straightforward
Just let me give you a simple way to look at it
The nullity is all inputs that give a 0 output
The range is all possible outputs
That’s always the case
dusk moon
The nullity is all inputs that give a 0 output
that's Ax=0 right
tacit elm
that's Ax=0 right
Yes
So all inputs (x) such as the output (Ax) is 0
So all inputs that lead to a 0 output
dusk moon
Nullspace is kinda weird though I found a non zero vector once that was in the nullspace
dusk moon
if nullity is non zero why is that important
tacit elm
if nullity is non zero why is that important
That means that A is singular
Meaning it loses dimensions
Let’s try the other example
dusk moon
I've also seen this definition of range of a matrix is the span of the columns of the matrix
tacit elm
Yes