-infinity and -1
#help-19
woeful rivet
wooden python
you have to include () or [] in interval notation always
woeful rivet
you have to include () or [] in interval notation always
oh yea
(0,infinity) and (-infinity,-1]
wooden python
not "and" but union
woeful rivet
oh yeh but why is their answer like that
wooden python
they decided to put it in set builder notation instead of interval notation
woeful rivet
oh ok thx
odd edgeBOT
@woeful rivet Has your question been resolved?
odd edgeBOT
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red tangle
Q15 chat
red tangle
A bag contains 5 red, 3 blue, and 2 green balls. Two balls are drawn without replacement. The probability that they
are of different colors is:
nocturne mica
what are your initial thoughts
red tangle
5/10 chance for a red ball 3/10 chance for a blue ball and 2/10 for a green one
For the first ball taken out
nocturne mica
casework
red tangle
What's that
nocturne mica
consider each case separately
red tangle
Okay
nocturne mica
in this case (heh) you have 3 cases to think of
to be more structured, you have two ways of looking at this problem
red tangle
Yes
nocturne mica
one is to calculate the probablity of drawing each possible combo of differing colored balls
the other is to use the complement method
red tangle
one is to calculate the probablity of drawing each possible combo of differing c...
I feel like this will take alot of time
nocturne mica
then complement method it is
red tangle
What is that
nocturne mica
given the stipulation in the question, what kind of situation are we trying to avoid?
red tangle
having two balls of the same colour
nocturne mica
excellent
red tangle
Thank you
nocturne mica
overall, the probability of drawing two balls without condition is 1, p sure you agree
red tangle
What's 1, p
nocturne mica
1 is the maximum overall probability for an event space
red tangle
Yes
nocturne mica
p = pretty
red tangle
Yes
nocturne mica
so our target probability is (probability of drawing 2 balls without conditions) - (probability of drawing 2 same-colored balls) = 1 - P(draw 2 same-colored balls)
agreed?
nocturne mica
this is the crux of the complement method
we find our desired probability by taking the total probability, and then removing all probabilities of events we don't want
whatever remains must be the probability of the events we are interested in
now
the challenge is to find P(2 same-colored balls)
nocturne mica
casework helps here
nocturne mica
case 1: say we drew a red ball up first.
our condition requires us to draw two balls of the same condition. by this stipulation, what must be the second ball's color in this case?
red tangle
Red
red tangle
1/2
nocturne mica
don't simplify yet
red tangle
5/10
nocturne mica
state them as they are
good
now, after drawing the first red, how many balls are left, and of them how many are red?
red tangle
9 balls left, 4 are red
nocturne mica
so the probability of drawing another red ball would be?
red tangle
4/9
nocturne mica
cool
so the overall probability of drawing two reds in a row from the start is...?
red tangle
5/10 × 4/9?
nocturne mica
correct!
red tangle
Hell yeah
red tangle
Hell yeah
nocturne mica
what about the green balls?
red tangle
2/10 × 1/9
red tangle
Mb
nocturne mica
(prefer sending a new message over editing. sometimes we can miss edits because we are not notified on an edit)
anyway
red tangle
(prefer sending a new message over editing. sometimes we can miss edits because ...
Okay
nocturne mica
now you have gotten the probabilities for each individual case
we know we don't want any of them
red tangle
Yes
nocturne mica
so we don't want (red AND red) OR (blue AND blue) OR (green AND green)
red tangle
Yes
nocturne mica
if you multiplied probabilities when there is an AND, what do you do when there is an OR?
nocturne mica
no
red tangle
Subtract?
nocturne mica
no again
nocturne mica
i was looking for just add
nocturne mica
you're not at the subtracting part yet
but close
anyway, so now you know you need to add up all of these probabilities
but we don't want them, and at the start we said we can do 1 - (this whole probability)
got your attack plan now?
red tangle
Yes
nocturne mica
go ham.
red tangle
Hell yeah
nocturne mica
well done. anything else?
nocturne mica
simplify
nocturne mica
hm
red tangle
I think the question is wrong
The answers
I can use this method in all problems right?
nocturne mica
generally yes, but you have to be smart about defining the complement of the events
red tangle
My teachers been giving me too many wrong questions lately
I think this is a test
I will discuss this with him
nocturne mica
at least show your working first though
show that you understood the requirements of the question
red tangle
at least show your working first though
Yes
I don't wanna nag him too much tho, he seems really depressed
nocturne mica
you don't have to call him out harshly, yk
just let him know that there's a mistake in the question
red tangle
you don't have to call him out harshly, yk
He would beat my ass up if I do that anyway
red tangle
just let him know that there's a mistake in the question
Yes
nocturne mica
if he didn't make your life difficult, you don't have to make his difficult
anyway
any other math questions?
red tangle
if he didn't make your life difficult, you don't have to make his difficult
I will write this down
odd edgeBOT
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Available help channel!
noble solstice
1st image is the question, 2nd image is the answer.
To answer this question I first supposed that 2 of the 3 peppers picked were orange, therefore the 3rd pepper I need to pick from can either be Yellow (2 peppers remaining) or Orange (3 peppers remaining); Therefore the probability is 3/2+3 = 3/5.
Somewhere my reasoning failed as the correct answer is 1/3, and I fully understand and follow the reasoning given in the book.
noble solstice
The rest of the question isn't needed for this problem if i read it correctly, here it is just in case:
(Please ping me!, thanks :))
odd edgeBOT
@noble solstice Has your question been resolved?
mental lotus
1st image is the question, 2nd image is the answer.
To answer this question I f...
your reasoning implies
either be Yellow (2 peppers remaining) or Orange (3 peppers remaining)
these two events are equally likely. Can you explain why 2 orange peppers remaining has the same chance as 3 orange peppers remaining?
Its the same kind of logic when people say tomorrow is either sunday or not, so 50% chance its sunday
noble solstice
Sorry I'm not really following, why does my reasoning imply that?
2 Orange peppers remaining and 3 orange peppers remaining are not equally likely as the first implies I picked 3 orange peppers meanwhile the last implies i picked 2 orange peppers and 1 yellow pepper, which are not equally likely events
"Given that 2 peppers are orange" means that I only have one more pepper to pick, this last pepper can either be yellow (2/5) or orange (3/5)
I'm so confused 
<@&286206848099549185>
odd edgeBOT
@noble solstice Has your question been resolved?
odd edgeBOT
@noble solstice Has your question been resolved?
noble solstice
<@&286206848099549185> anyone :3
golden sonnet
1st image is the question, 2nd image is the answer.
To answer this question I f...
PnC weak😔
cant help
noble solstice
all good :}
desert jacinth
very interesting probability
I sadly cannot help but it is nonetheless interesting
noble solstice
I sadly cannot help but it is nonetheless interesting
np!
desert jacinth
interesting isn't the word i'd use
how would you describe it
desert jacinth
I did some probability last year, what we learned is some formulas related to it, all I can say is that you could use them I guess 😭, I really don't remember them myself!
desert jacinth
confusing lol
I agree
signal yacht
ok OP do you know any conditional prob
noble solstice
ok OP do you know any conditional prob
Yep
I mean the issue is that I understand how to solve the problem correctly, I'm just not sure what is incorrect with my solution
Like I know how to solve the question, I just used a different method which gives me a wrong answer, but I can't find the error in my reasoning
And it's frustrating cause this happens all the time with probability and it's usually something small and dumb
signal yacht
ah
ok
i do not understand what you mean by 'Therefore the probability is 3/2+3'
i do not follow
noble solstice
After picking 2 orange peppers, i have one more pepper to pick, the probability that this last pepper is orange, is the number of favourable outcomes (3) divided by the number of total possible outcomes (5), so 3/5
autumn bolt
After picking 2 orange peppers, i have one more pepper to pick, the probability ...
and what are the 5 outcomes
according to you its first two orange and then any pepper
i think we assume that the peppers are distinct here
only then will 1/3 be valid
and you have gotten 3/5 with one of the assumptions being that all peppers with the same color are identical
noble solstice
huh
yea that does make sense
yea i thought about it for a while and it does make my reasoning incorrect cause now which first two peppers i pick matters even if they are both orange
thanks! @autumn bolt
.close
odd edgeBOT
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Available help channel!
ruby sundial
I’ve made it this far, but I truly have no idea what steps to take from here,
ruby sundial
My goal it to find the exact value, which is (720/1681 according to the answer sheet)
olive needle
<@&268886789983436800>
stoic cloud
<@&268886789983436800>
sage rapids
oh my
ruby sundial
What was that?
vernal yacht
That was horrendous
brazen hare
I’ve made it this far, but I truly have no idea what steps to take from here,
imagine a right-angled triangle with a leg of 9 and a hypotenuse of 41 :)
then label where x would be
actually wait you already found sin x and cos x
you can just substitute it in no?
ruby sundial
you can just substitute it in no?
I don’t see how, I’m sorry
brazen hare
I’ve made it this far, but I truly have no idea what steps to take from here,
You let $x = \cos^{-1}(\frac{9}{41})$ and wrote down that $\sin(2x) = 2\sin(x)\cos(x)$
clever fjordBOT
brazen hare
on the last two lines you found what $\sin x$ and $\cos x$ are equal to
clever fjordBOT
ruby sundial
Yeah,
brazen hare
so...? just put the fraction you found for sin x and cos x into 2 sin x cos x
ruby sundial
Oh snap you’re right
Sorry for the trouble, I think I’ve been staring at it for too long
Thank you,
.close
odd edgeBOT
brazen hare
it's alright
shell haven
it's alright
I guess we're both nocturnal
odd edgeBOT
Available help channel!
slender turtle
How would i study the variations of |1+1/x|^x on its domain ?
slender turtle
Its derivative is too annoying to manipulate for that
Ideally ud solve for f'>0 and such but not there then
summer wave
maybe studying the log of that is easier
odd edgeBOT
@slender turtle Has your question been resolved?
slender turtle
maybe studying the log of that is easier
Still have sm too hard to manipulate
cerulean vortex
well i can get it in terms of W(1/e) where W is the lambert W function,
and W(1/e) doesn't appear to be listed among the special values of the lambert W function, which means you probably can't simplify it
,w 1/(1+LambertW(1/e))-1
clever fjordBOT
odd edgeBOT
@slender turtle Has your question been resolved?
odd edgeBOT
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Available help channel!
manic grail
hello
manic grail
what does about x=a mean
faint knot
"about x = a" means the x - a part of the series
about x = 0 would mean x^n
about x = 1 would mean (x - 1)^n
etc.
a series with (x - a)^n converges in a small area around x=a
odd edgeBOT
@manic grail Has your question been resolved?
manic grail
"about x = a" means the x - a part of the series
im confused
what does he mean about x=a
faint knot
do you want more meaning out of the a for (x - a)^n?
manic grail
yea thats the general case
faint knot
what do you get
manic grail
c0
faint knot
and so f(a) = c0
manic grail
yes
faint knot
so for this series, f(a) is what you get if you put in a into an (x - a) formula
similarly, what would f'(a) be?
manic grail
no but
on the picture
he says that
and proceeds to not use x=a
thats why im confused
here he is keeping it as a function
faint knot
good job cutting off the image before that matters then
manic grail
what
faint knot
you need to show the rest of the stuff before we can be sure the x=a or (x - a) stuff doesnt matter
faint knot
and proceeds to not use x=a
wdym by this
manic grail
like he says about x=a
faint knot
yea?
manic grail
but then doesnt say f(a)
faint knot
thats not what "about x = a" means
we already said this
"about x = a" is how you say out loud the series using (x - a)^n
faint knot
for example, "about x = 1" is for a series using (x - 1)^n
and "about x = 0" is for a series using x^n
manic grail
but i dont understand the notation
faint knot
I am literally explaining it to you right now
manic grail
why not say for the general form of the power series
manic grail
I am literally explaining it to you right now
ok but i dont understand like why we say x = a
faint knot
you dont need to see the word "general" to use context clues and see that its the general form
manic grail
thats a picked value
faint knot
no it isnt
manic grail
how is x = a not choosing a value for x?
manic grail
its a question
faint knot
have you seen the word "about" being used like this before
manic grail
about x=a just seems wrong to say to me
manic grail
have you seen the word "about" being used like this before
nah not really
faint knot
have you learned function transformations yet?
manic grail
have you learned function transformations yet?
wdym
faint knot
its a question
manic grail
as in linear transformations?
faint knot
have you reflected a shape on a graph before?
manic grail
in linear algebra yes
manic grail
i just answered
faint knot
this isnt linear algebra
this is just regular algebra
have you learned this in regular algebra before
manic grail
yes
faint knot
there is more than one way to say "over the x-axis"
you can also say something like "over y=0"
similarly, "around y=0" or "about y=0"
these all mean the same thing
manic grail
oh
faint knot
it means to treat y=0 as the center of something happening
manic grail
maybe straight translation to my language doesnt help thats why
faint knot
this is just a strange way to say things where about is used as a preposition
manic grail
cause its similar to for x=a
faint knot
similarly, "around y=0" or "**about** y=0"
you have to recognize "about <noun>"
manic grail
but i see how you mean its used
faint knot
yea, its a specific kind of usage for about
most likely youll only ever see it in math
manic grail
so
faint knot
using it like that should mean to do something with <noun> as like a center
manic grail
about x=a
faint knot
so "about x = a" means "centered at x = a"
manic grail
means with the center of the radius of convergence being a
faint knot
yep
manic grail
ok
faint knot
this is btw different from the usual usage of about
if you say "how about x = a" that will just mean to plug in x = a
manic grail
this is btw different from the usual usage of about
yes ik thats why i was confused
faint knot
youll just have to get used to these strange usage of words as they come up
manic grail
sorry i havent studied math in english for long so im still adapting to terminology
manic grail
yea ok makes sense now
manic grail
thank you
manic grail
I dont think a machine translation wouldve figured this out
yes it doesnt
faint knot
honestly I dont know how youd find this out otherwise
your best luck I think is to read the context to see what "x=a" is being treated as
that way you can learn the usage of about as being like this
manic grail
yea i thought of it
faint knot
but given this is probably your only example, you dont have enough to go off of
manic grail
ok appreciate your help
faint knot
np
odd edgeBOT
odd edgeBOT
Available help channel!
bold ingot
i am an first year ug engineering student
warm horizon
hello everyone i want the fastest way to master number theory to enter IMB and i have read most of introduction to number theory published by AOPS so please help
robust condor
as a beginner, the videos of 3blue1brown are very good
https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab
bold ingot
as a beginner, the videos of 3blue1brown are very good
https://www.youtube.com/w...
thank you
twin vigil
as a beginner, the videos of 3blue1brown are very good
https://www.youtube.com/w...
but i don't think there is explanation of properties and small notes
warm horizon
hello everyone i want the fastest way to master number theory to enter IMB and i have read most of introduction to number theory published by AOPS so please help
bold ingot
i have watched it already
twin vigil
hello everyone i want the fastest way to master number theory to enter IMB and i...
maybe use MONT,
warm horizon
maybe use MONT,
what is this??\
twin vigil
what is this??\
its a book of number theory by evan chen i beleive
bold ingot
hello everyone i want the fastest way to master number theory to enter IMB and i...
this is occupied 😭
twin vigil
but i need a detailed explations
there is good video on MIT OCW just search matrix and determinants MIT OCW on youtube and learn the properties and find practice problems on internet
or from any linear algbera book
robust condor
hello everyone i want the fastest way to master number theory to enter IMB and i...
maybe you can ask another question on "Available" up here, like help-30, help-47
bold ingot
for reference i have to study all this for my first sem
warm horizon
maybe you can ask another question on "Available" up here, like help-30, help-47
Sorry i am new at the group
robust condor
Oh, I think there are many "deep knowledge", maybe about "matrix analysis"
bold ingot
there is good video on MIT OCW just search matrix and determinants MIT OCW on yo...
okay thank you
bold ingot
Oh, I think there are many "deep knowledge", maybe about "matrix analysis"
on youtube
robust condor
As a math student, I have not learn too much of these on "Linear algebra course".
bold ingot
are there any books for beginners on linear algebra / applied math?
more of a theory based
robust condor
There are differences in learning focuses, between engineering and math major. I think a time saving way is just to learn these specific topic, but I didn't learn specifically. Sorry for no more suggestions
bold ingot
There are differences in learning focuses, between engineering and math major. I...
what if i dont wanna learn specifically but the whole of it ? any ideas?
robust condor
there is good video on MIT OCW just search matrix and determinants MIT OCW on yo...
I think @twin vigil 's suggestion is good enough, I've heard that the MIT Linear algebra courses are excellent
odd edgeBOT
@wooden oar Has your question been resolved?
odd edgeBOT
@wooden oar Has your question been resolved?
honest turtle
Du har mest sannsynlig blitt introdusert til formelen $$a_1 \frac{r^n-1}{r-1}$$ Ifølge teksten har hun et lån på 2 200 000, og rente på 3.1%, som vil si at uttrykket til høyre er det totale som May skal betale tilbake. Formelen til venstre brukes til å regne dette ut (se gjennom sidene du har sett, det er mest sannsynlig noen eksempler som gjør deg mer kjent med formelen).
clever fjordBOT
Good
odd edgeBOT
@wooden oar Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
tepid patrol
Hi guys, I'm training on proofs with induction, the exercise is"Prove by induction that for every n \in \mathbb{N}, n \geq 3, n! \gt n+2"
I find myself stuck cause I dont know how to do proofs and I'm trying to learn, you'll see all the steps I did in the following pictures, if anybody got any advice on how to keep going with the proof it would be really appreciated! Thank you
summer wave
it's good to keep in mind what you are trying to prove
you want $(n+1)! > (n+1) + 2$
clever fjordBOT
bloubbloub
summer wave
currently you have $(n+1)! > n^2 + 3n + 2$
clever fjordBOT
bloubbloub
tepid patrol
Oh so the way I wrote (n+1)(n+2) is wrong right?
Honestly I dont understand if I have to "multiply" or "add up
summer wave
you're supposed to multiply
tepid patrol
For example, if I have $n! > n+2$
clever fjordBOT
Shlik Shlak Shluk
tepid patrol
Does it have to be $(n+1) multiply n! > (n+1) multiply n+2$?
clever fjordBOT
Shlik Shlak Shluk
tepid patrol
Or does it have to be $(n+1)n! > n +1 +2$
clever fjordBOT
Shlik Shlak Shluk
summer wave
**Shlik Shlak Shluk**
you need to show this
summer wave
**Shlik Shlak Shluk**
currently you have this
tepid patrol
So whenever I'm doing induction proof, in the inductive step, I have to multiply the whole left part for (n+1) and the same goes for the right part?
summer wave
hm
there is no general rule for the inductive step
but you need to use your induction hypothesis yes
tepid patrol
Im kinda confused then... cause the first tiem I was solving the exercise, what I wrote was
tepid patrol
**Shlik Shlak Shluk**
this
I was lucky that $(n+1)n!$ is equal to $(n +1)!$ otherwise I would have made it wrong u know? So I'm just trying to understand what should I write in these situations
clever fjordBOT
Shlik Shlak Shluk
summer wave
you say you're lucky but in reality the problem statements are made so you can actually prove things
so im not sure what you mean
tepid patrol
I'll try to draw it just a moment
The last part
I'm asking whats the right way to solve the exercise
Since I think the last one is wrong
But that was the way I was trying to solve the exercise at first try
summer wave
can you make any statement about n+3 and (n+2)(n+1)?
tepid patrol
I can tell that (n+2)(n+1) is greater than n+3
summer wave
then you just need to write that
tepid patrol
Sorry I can't explain myself due to language barrier I think... what I mean is that the way I would have solved the exercise, is the second point aligned with "Wrong"... I understood that is wrong because I talked with you and because I tried to look for the solution on internet, so my question is... for every induction proof exercise that I'm going to do, in this case for the inequality n! > n+2, do I have to always use the first method "Right"?
tepid patrol
Ok thank you.. btw I think I understood how to solve it, I'll send u a drawing rq
Do you think it makes sense this way mate?
odd edgeBOT
@tepid patrol Has your question been resolved?
tepid patrol
<@&286206848099549185>
summer wave
you need to show that (n+1)(n+2) >= n+3
tepid patrol
you need to show that (n+1)(n+2) >= n+3
? Why is that? I'm not understanding the reasoning sorry :c
summer wave
you should at least mention it
otherwise you would not have finished the induction step
tepid patrol
you should at least mention it
I need to mention (n+1)(n+2) because is the inductive step right? But what about n+3?
summer wave
you're supposed to show that (n+1)! > n+3
for that, you can say that (n+1)! > (n+1)(n+2) > n+3
but I think you need to justify the 2nd inequality
tepid patrol
I understand why should I show that (n+1)! > (n+1)(n+2), since it can helps with proving the inductive step (n+1)n! > (n+2)(n+1) right? But what about n+3? I'm kinda confused about it
summer wave
the induction hypothesis is n! > n+2
so you need to prove this with n <- n+1
that would be (n+1)! > (n+1) + 2
tepid patrol
so you need to prove this with n <- n+1
Why this?
summer wave
in the inductive step, you suppose that n is an integer such that n! > n+2. You need to prove that (n+1)! > (n+1) + 2
it's like dominos
'if it's true for n, then it must be true for n+1"
you need to show that
tepid patrol
in the inductive step, you suppose that n is an integer such that n! > n+2. You...
Yes, I do agree and understand this
But I'm not understanding the point about n < - n+1
clever fjordBOT
bloubbloub
tepid patrol
Oh ok sorry, so you're saying that i have to prove the induction hypothesis n! > n+2 first with n -> n+1 right?
summer wave
you need to prove it with n+1 yeah
tepid patrol
Which I tried to do here, what did I do wrong?
tepid patrol
Sorry, what I meant there was that n! > n + 2 \implies (n+1)n! > (n+2)(n+1) because n! > n+2 since we proved that in the base case, and what remains is (n+1) which is in the both sides, so we can "delete it"
I think its wrong since it's exactly what I just wrote... so it makes no sense.. sorry
I just understood it now.. but I'm really s tuck
Also it doesnt make sense cause I'm multiplying(n+1) for different numbers so I cant tell anything, sorry
summer wave
$$n! > n + 2 \implies (n+1)n! > (n+2)(n+1)$$
and $$(n+2)(n+1) = (n+1) + (n+1)^2$$. \
Since $n \geq 3$, we know that $(n+1)^2 > 2$, so $(n+2)(n+1) > (n+1) + 2$
clever fjordBOT
bloubbloub
summer wave
Therefore $n! > n + 2 \implies (n+1)n! > (n+1) + 2$
clever fjordBOT
bloubbloub
summer wave
that's the induction step
tepid patrol
Sorry if I'm taking a while to answer, I'm trying to make it "make sense" in my head
I'm not understanding why we're doing $(n +2)(n+1) > (n + 1) +2$
clever fjordBOT
Shlik Shlak Shluk
tepid patrol
If you have any video or note that I could read as advice it would also be nice
fringe cradle
You been at it for 3hrs
oak crown
I'm not understanding why we're doing $(n +2)(n+1) > (n + 1) +2$
$(n+1)n!=(n+1)!$, and we know that $(n+1)n!>(n+2)(n+1)$. Our inductive step is to show that $(n+1)!>(n+1)+2=n+3$. So we want to show that $(n+1)n!=(n+1)!>(n+2)(n+1)>n+3$ to prove our inductive step.
clever fjordBOT
;(
tepid patrol
**;(**
How do we know that $(n+1)n! > (n+2)(n+1)?
Aren't we trying to prove it for the inductive step?
mystic saffron
and by the principle of mathematical induction, the inequality n! > n+2 is true for all integers n≥3. I hope it's correct
tepid patrol
Ty for all the clear notes mate I'm reading them slowly trying to catch the right points
mystic saffron
You been at it for 3hrs
everyone moves at their own pace
summer wave
for the inductive step, you need to prove that (n+1)! > n+3, not (n+1)n!>(n+2)(n+1)
mystic saffron
for the inductive step, you need to prove that (n+1)! > n+3, not (n+1)n!>(n+2)(n...
it is not the final goal itself, but a crucial intermediate step to get to that goal by using the definition of factorial
summer wave
Aren't we trying to prove it for the inductive step?
for this
tepid patrol
Why in the second page are we trying to prove that $(k+1)! > n+3$ instead of trying to prove $(k+1)! > k^2 + 3k +2$ ?
clever fjordBOT
Shlik Shlak Shluk
summer wave
for the inductive step, you need to prove that (n+1)! > n+3, not (n+1)n!>(n+2)(n...
this
summer wave
because the inductive hypothesis is n! > n+2
you want to prove the induction hypothesis for n+1
tepid patrol
Yea
summer wave
the induction hypothesis for n+1 is "(n+1)! > n+3"
tepid patrol
But if we multiply for n+1 we dont find n+3, am I wrong?
summer wave
no you're not
tepid patrol
Aren't we trying to prove:
Case base: that n ! > n + 2
and
Inductive step: that (n + 1)! > (n + 1)(n + 2)?
Okay wait.. maybe I understand your point
Since we know that (n + 1)! is 100% greater than (n+1) we want to make sure is greater than (n + 2) so that we can define it greater for both of them? 😭
At this point I dont understand anymore lol
mystic saffron
Aren't we trying to prove:
Case base: that n ! > n + 2
and
Inductive step: tha...
gimme some minutes 🙂
tepid patrol
base case: 3! > 3 + 2
inductive step: n! > n+2
Yes I agree with the base case
But isn't the inductive one n+1?
summer wave
maybe I worded it wrong
base case: 3! > 3 + 2
inductive hypothesis: n! > n+2
inductive step: n! > n+2 \implies (n+1)! > (n+1) + 1
mystic saffron
But isn't the inductive one n+1?
just another 5 minutes bro..
tepid patrol
just another 5 minutes bro..
np, thank u man
Was just talking about it with him too
mystic saffron
np, thank u man
I’m not a man 😁
tepid patrol
I’m not a man 😁
Mate* :)
Ty for the pdf my friend
I'm checking it now
oki thank u so much for the pdf
I think ur notes are enough, I'll just keep looking at them and studying them
Without keeping this channel longer
So that others can get help in the meanwhile
What do u think? :)
mystic saffron
ok I’m not sure if you’re just being nice or honest, but yes you’re right! Best of luck 🫶🏻
tepid patrol
ok I’m not sure if you’re just being nice or honest, but yes you’re right! Best ...
Both lol
Its not 100 % clear but mate, you did a lot already and thank u to both of u for the patience, I just need more work into it @mystic saffron @summer wave
How to end the help here?
summer wave
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tepid patrol
.close
odd edgeBOT
tepid patrol
ty guys
odd edgeBOT
Available help channel!
plucky root
47
plucky root
,rccw
clever fjordBOT
plucky root
,rccw
clever fjordBOT
clever fjordBOT
clever fjordBOT
plucky root
convert to sin and cos
I did
plucky root
then kings rule
Is it usefull here?
solar peak
obviously
plucky root
It's pi/4 and pi/6
plucky root
Oki
odd edgeBOT
@plucky root Has your question been resolved?
leaden karma
How do I solve the recurrence [ a_{n+1} = 1 + b_n\pi\lambda, \quad b_{n+1} = a_n\pi\lambda \text{ for } n>1, \quad a_0 = 1, b_0 = 0 ]
clever fjordBOT
kheer257
leaden karma
here lambda is a constant
It comes from the second part of this question, where I assume the form of $y_n(x)$ to be $y_n(x) = a_n \sin(x) + b_n \cos(x)$ and get these recurrences
clever fjordBOT
kheer257
leaden karma
I can get a second order recurrence in $a_n$, since $a_{n+2} = 1 + b_{n+1}\pi\lambda = 1 + \pi^2\lambda^2 a_n$
clever fjordBOT
kheer257
south plume
odd edgeBOT
south plume
quick question, what exactly is the difference between (1) and (2)?
delta is the Dirac delta
(1) says that for all finite t, delta(t) is non-negative
(2) says that for all non-zero t, delta(t) is 0
wut
woeful briar
the first one is kind of useless
woeful briar
but I guess its because they want to use theorems that only work on positive functions using this
south plume
but I guess its because they want to use theorems that only work on positive fun...
thanks!
.close
shy bronze
do i have to differentiate all the answer choices to check?
serene torrent
Please try to learn more about the topic first. I see that you may need help but asking this much questions is not right. We can help about a topic to solve many questions but we can't help with solving them one by one.
shy bronze
.solved
lone hatch
odd edgeBOT
lone hatch
For question 4), why is it wrong to pick an even number and then pick any number from the entire set i.e.
10C1 x 19C1 and then /2! for arrangements
forest sky
,rccw
clever fjordBOT
lone hatch
For example in question 3), I did 10C1 x 9C1 then /2! instead of their way
But I couldn’t apply it to 4
More specifically I did 10C1 to pick an initial even number and an even number times any integer is even so I can then choose from the remaining set which is 19 so 19C1 and then /2! for when the even is first or second
forest sky
in 3) you could divide by the number of arrangements of 2 numbers because each possibility does appear twice (once in each order) whereas in 4) only some possibilities appear in both orders
lone hatch
in 3) you could divide by the number of arrangements of 2 numbers because each p...
I think I get what you mean but could you explain a bit more
Since we’re multiplying it shouldnt matter which number is pulled first or second right?
The textbook is wrong
forest sky
yes, it shouldn't matter. but when we divide by 2! that would be to compensate for overcounting by having each possible ordering of pairs appear, e.g. we have both (2,4) and (4,2) in our setup
but (2,1) only appears once so it isn't overcounted
lone hatch
but (2,1) only appears once so it isn't overcounted
Ohhh
That makes sense
I think I found a mistake in the textbook but I wasnt sure
For case 4b when they do the ways for odd x even
10C1 x 10C1,
Did they not forget to account for arrangements by dividing by 2!?
So in case 4b theyre counting even x odd and odd x even as separate permutations
And if you divide by 2 for the 100 ways its 50 and then + 45 you get 95 total arrangements
Which is the same as 10C1 x 19C1 / 2!
but youre right that we also need to account for the case where it only appears once like (2,1)
forest sky
accounting for arrangements is compensating for the fact that the same pair of numbers appears twice (once in each order). but in this case you can get (1,2) but can't get (2,1) so it isn't overcounted like that
since there aren't any numbers which are both odd and even we can't get any repetition
lone hatch
accounting for arrangements is compensating for the fact that the same pair of n...
Ohh it just clicked
I understand
I was thinking that you could switch the set you pick from first like odd even or even odd but then that would be another case and we didnt account for that so its not doubled
thanks
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odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
I understand the it is a converging infinite sum . Having us finding area1 and r. I haven’t freshed up on circle geometry so I’m stuck in finding the needed distance so I can find the radius so I can find the area so I can plug and find r so I can find the area of the second circle.
odd edgeBOT
I understand the it is a converging infinite sum . Having us finding area1 and r...
@mystic saffron Has your question been resolved?
upbeat stump
I understand the it is a converging infinite sum . Having us finding area1 and r...
Wait I’m trying but I can’t get the right answer lmaoo
cerulean vortex
i'm getting $\frac{x}{3\sqrt{3}}$
clever fjordBOT
Axe
upbeat stump
Damn so we all fumbling💔
cerulean vortex
weird, i got the total area $3\pi x^2 / 8$
clever fjordBOT
Axe
upbeat stump
Omg this question is so weird
Do u think we can assume B is the center of the first circle?
cerulean vortex
yes
upbeat stump
Right then I can’t see where I went wrong at all😭😭😭😭
Ight fuck it I give up💀🙏
Thanks for ur help dude
.close
odd edgeBOT
odd edgeBOT
Available help channel!
fleet lake
odd edgeBOT
vernal yacht
,rotate
clever fjordBOT
fleet lake
So it's 29
fleet lake
,rotate
Range type question ig
So I'll convert them into cos
Cos2x+2 into cos^2 x+1
It's cos 2 -1
Always -ve who hoo
D
.close
fleet lake
30
fleet lake
,rccw
clever fjordBOT
fleet lake
.close
upbeat stump
What they mean by upper bound?
odd edgeBOT
What they mean by upper bound?
upbeat stump
.close
bold shard
Could someone teach me how to divide radicals from the basics to the rationalizing monomial square roots and conjugating binomial DoS
atomic hornet
Could someone teach me how to divide radicals from the basics to the rationalizi...
what is DoS?
bold shard
what is DoS?
Difference of squares
atomic hornet
Let's clarify, you'd like to know how to change $a^2 - b^2$ into $(a+b)(a-b)$, am I correct? And another question is how to transform $\frac{1}{\sqrt{x}} $ into $\frac{\sqrt x}{x}$
clever fjordBOT
This is sad 😢
atomic hornet
@bold shard
bold shard
Let's clarify, you'd like to know how to change $a^2 - b^2$ into $(a+b)(a-b)$, a...
Yes
Sorry for the wait!
atomic hornet
Sorry for the wait!
no worries, are you ready for the explaination?
Ping me when you're back, then I'll begin with rationalization
atomic hornet
Alright!
bold shard
Cool
atomic hornet
First of all, we have $\frac{1}{\sqrt{x+1}}$, to rationalize this, we basically multiply the numerator and the denominator by $\sqrt{x+1}$. The result would be $\frac{\sqrt{x+1}}{x+1}$. Do you agree so far?
clever fjordBOT
This is sad 😢
bold shard
mhm
atomic hornet
u sure?
bold shard
Yeah
atomic hornet
there will be some small quiz later
bold shard
I’m with you
atomic hornet
Alright
bold shard
there will be some small quiz later
I’ll try
atomic hornet
Can you do $\frac{x+2}{\sqrt{x+1}}$ for me?
clever fjordBOT
This is sad 😢
atomic hornet
It’s 1 am in the morning
You're so dilligent
atomic hornet
,rotate
clever fjordBOT
atomic hornet
There we go, what's the result?
bold shard
atomic hornet
,rcw
clever fjordBOT
atomic hornet
that question mark is just $\sqrt{x+1}$
clever fjordBOT
This is sad 😢
bold shard
Yes but I don’t know what I should next
atomic hornet
and yes, it cannot be simplified further
atomic hornet
Yes but I don’t know what I should next
nope, that's all
bold shard
oh
atomic hornet
rationalization is basically removing sqrt from the denominator
bold shard
The bottom the square root is gone
bold shard
Sure
atomic hornet
We've already done half of the task you mentioned
Alright
-
Rationalize the denominator:
[
\frac{5}{\sqrt{3}}
] -
Rationalize the denominator:
[
\frac{7}{2\sqrt{5}}
] -
Rationalize the denominator:
[
\frac{3}{\sqrt[3]{4}}
] -
Rationalize the denominator:
[
\frac{\sqrt{6}}{\sqrt{2} + \sqrt{3}}
] -
Rationalize the denominator:
[
\frac{2}{\sqrt{7} - \sqrt{5}}
] -
Rationalize the denominator:
[
\frac{1}{\sqrt[3]{2} + \sqrt[3]{4}}
]
clever fjordBOT
This is sad 😢
bold shard
Ok
atomic hornet
I just asked GPT for some sample questions cuz I'm too lazy to come up with some myself LOL. No worries, I'll verify your answers.
atomic hornet
correct
bold shard
14sqrt5/10?
atomic hornet
Try again
bold shard
Hm
The only question is if you multiply the radical, does that coefficient multiply with the radicand
atomic hornet
you made a very smol mistake
atomic hornet
The only question is if you multiply the radical, does that coefficient multiply...
Like the number in front of the sqrt? no
you just wanna rid sqrt out of the denominator, there's no need to disturb other residents there.
atomic hornet
$\frac{7}{2\sqrt{5}}$
clever fjordBOT
This is sad 😢
atomic hornet
Look, all you need is to multiply both sides by sqrt5
you don't need to touch other numbers
bold shard
What would rationalizing this equation look like
atomic hornet
$\frac{7}{2\sqrt{5}} = \frac{7}{2} \times \frac{1}{\sqrt 5}$
clever fjordBOT
This is sad 😢
bold shard
Aren’t you technically supposed to get rid of the radical tho
atomic hornet
No, you are trying to Move it up
bold shard
Okay
atomic hornet
Please lemme know if you feel uncomfortable when I'm explaining, since my tone may come off rude
minor crest
.
bold shard
Not really
lmao
Why am I thinking so hard about the third one
I’m assuming you multiply the top by 1
And the bottom with cuberoot4
vernal yacht
bold shard
How would you know whether if you should bring the radical towards both the top and bottom
minor crest
Hello
bold shard
Or only bottom
atomic hornet
How would you know whether if you should bring the radical towards both the top ...
keep in mind, the objective is to kick out every sqrt from the denominator
bold shard
Do you do it twice
atomic hornet
no, what did we do to $\frac{1}{\sqrt 2}$
clever fjordBOT
This is sad 😢
bold shard
Multiplied sqrt 2 to num and denom
clever fjordBOT
This is sad 😢
atomic hornet
Index doesn’t matter
what is index?
atomic hornet
Ohh
Alright, lemme demonstrate
gimme a min to latex it
[
\frac{1}{\sqrt[3]{2}}
= \frac{1}{2^{\tfrac{1}{3}}}
= \frac{1 \cdot 2^{\tfrac{2}{3}}}{2^{\tfrac{1}{3}} \cdot 2^{\tfrac{2}{3}}}
= \frac{2^{\tfrac{2}{3}}}{2}
= \frac{\sqrt[3]{4}}{2}
]
clever fjordBOT
This is sad 😢
bold shard
Oof
atomic hornet
bruh 😭
ya get it?
bold shard
Is the fractions supposed to be there
atomic hornet
which one?
bold shard
All
atomic hornet
yes
bold shard
Where’d you get 1/3
atomic hornet
you mean $\sqrt[3]{2}$?
clever fjordBOT
This is sad 😢
atomic hornet
$\sqrt[3]{2} = 2^{\frac{1}{3}}$
clever fjordBOT
This is sad 😢
atomic hornet
wdym
atomic hornet
**This is sad 😢**
Like doing this?
atomic hornet
no, I would get the answer myself
bold shard
And I have church 😭
atomic hornet
without this process
atomic hornet
And I have church 😭
bruhhhh, go for it. don't waste your time on Math
bold shard
bruhhhh, go for it. don't waste your time on Math
Yea
I’m geeked rn so
tired
aight peace mate
atomic hornet
Feel free to ping me next time if you wanna continue this
atomic hornet
I can’t concentrate
alright
bold shard
Feel free to ping me next time if you wanna continue this
Yep
odd edgeBOT
minor crest
or ping <@982507190566932510>
That's my main account
???
odd edgeBOT
Available help channel!
past spear
hi can someone help me on this
odd edgeBOT
hi can someone help me on this
late sinew
hi can someone help me on this
!Status
odd edgeBOT
hi can someone help me on this
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
im so confused i asked gpt and i stil dk
wooden python
!nogpt
odd edgeBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
wooden python
@past spear do you have an attempt of your own at all?
even if you got it wrong
show us anyway
sand horizon
and i got it wrong
What was it
wooden python
you may have done something right and we need to know
so that we can then tell you what to fix
or what to do in general
shell haven
hi can someone help me on this
Try expanding then comparing coefficients
shell haven
Owh-k
odd edgeBOT
atomic hornet
Sadge
atomic hornet
This is very sad 😢
odd edgeBOT
Available help channel!
hearty nest
odd edgeBOT
hearty nest
i m stuck
cinder lava
add 1 and subtract 1 from numerator
high cave
I forgot math
Im studying medicine 1st yr
I just came here seems like I totally forgot how to do this
wtf is my memory
high cave
bro what do u do
odd edgeBOT
cinder lava
bro what do u do
i used a property
hearty nest
yh
high cave
i used a property
Which one
nvm, Im not into math anymore I finished my high school Im Pursuing medicine rn
hearty nest
cinder lava
reef belfry
ke rani jo tu aaye is dil mai ho hal chal
reef belfry
Bargad tale intezaar tera, mai karu kab tak...?
hearty nest
chup
high cave
I learnt in shortcut
reef belfry
study bio bro
high cave
substitution method
reef belfry
why tryna get into maths if u done
high cave
why tryna get into maths if u done
just for fun
high cave
*Bargad tale intezaar tera, mai karu kab tak...?*
wot
high cave
*ke rani jo tu aaye is dil mai ho hal chal*
what are u talking about man
why do u speak like minecraft enchantment table
reef belfry
bro its just a song
high cave
oh Im sry
hearty nest
🤣
reef belfry
im obsessed
high cave
im obsessed
in math?
reef belfry
with that song
reef belfry
why are u sorry
cinder lava
hearty nest
yh its fine
reef belfry
yh its fine
paglu