help-10

[fathom kindle]

oh so theres a horizontal asymptote but

no vertical one?

i thought it just goes up infinitely

or it still like goes to the right

ye

.close

[obtuse pebble]

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[tribal bloom]

I don't understand this one at all

Do I multiply each coordinate of the vertex?

Which is (8,-6)?

.close

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[strong kestrel]

s

[latent walrus]

hm?

[strong kestrel]

ik a

but some guy was helping me out with the following

but b is what got me the most

[latent walrus]

whats up with b

[strong kestrel]

so I know that g(a) is 4, however it isn't define in this case. but limg(x) is. So I am confused into like finding the limit of this

or the point

or whatever Im looking for

[restive gorge]

there is no g(a) is 4

i also dont know why the channel got closed lol

[strong kestrel]

yeah that's what I was thinking too

oh yeah mb

G(4)

right?

[restive gorge]

for b) in simple terms look for a value of x where from both sides you approach the same limit, but at that limit the value has a circle

[restive gorge]

for b) no

[strong kestrel]

a I mean

[restive gorge]

yes

for a) correct

a = 4

[strong kestrel]

idk but is it still 4?

[restive gorge]

No

[strong kestrel]

or 2

[restive gorge]

don't guess

Again

[strong kestrel]

yeah mb

5?

[restive gorge]

yes

but explain

i cannot make it more simpler

limit exists if from both sides your approach the same value

[strong kestrel]

bro

so

omg

thank you for telling me this

[restive gorge]

what

[strong kestrel]

my professor hasn't told me that

[restive gorge]

[strong kestrel]

ok so im getting it know

the fact that its 5 is due to the fact that both sides meet up at a undefined point

[restive gorge]

yea lmao

what happened to you

[strong kestrel]

bro

Im literally on my notes looking for this infoormation

[restive gorge]

brain sparked

[strong kestrel]

I mean yeah

[restive gorge]

well then c)

[strong kestrel]

its 2 and 4

2 is the one coming from the left, while 4 is the one coming from the right

or 2 is the minus and 4 is the plus

[restive gorge]

yes you are right

[strong kestrel]

ooh

you got me thinking hard for a seccond

[restive gorge]

i read c) wrong

you are right

[strong kestrel]

i have a question tho

[restive gorge]

sure

[strong kestrel]

oh wait nvm

[restive gorge]

brain sparked again

[strong kestrel]

I was about to ask why couldn't it be a singular value since their coming from both ways

[restive gorge]

what

[strong kestrel]

but lim g(x) DNE

[restive gorge]

ah

[strong kestrel]

yeah

and then

d

[restive gorge]

If you also didn't know

[strong kestrel]

is 4

[restive gorge]

yea

[strong kestrel]

because it's a plus and g(4)

[strong kestrel]

yeah wsp

[warm shale]

bacc

[strong kestrel]

yeah

and if isnt

then its DNE

[restive gorge]

in case your professor has another profession

[restive gorge]

yea

[strong kestrel]

dam well thank you man

[restive gorge]

thank yourself

[strong kestrel]

I appreciate your help

[restive gorge]

thanks

[strong kestrel]

wait btw

[restive gorge]

https://tenor.com/view/luigi-super-mario-n64-sm64-render96-gif-27115141

[strong kestrel]

cause I have a calc exam next week. Do you know any good youtube videos about calculus

[restive gorge]

uhm

[strong kestrel]

or any other resources

[restive gorge]

calculus is kinda big and vague

[strong kestrel]

ok

[restive gorge]

is it calc 1 or calc 2?

[strong kestrel]

well specifically like limits, laws of limits and discontinuity

calc 1

[restive gorge]

oh

[strong kestrel]

Im like in the intro of calculus

[restive gorge]

The Organic Chemestry is good

https://www.youtube.com/watch?v=GiCojsAWRj0&list=PL0o_zxa4K1BWYThyV4T2Allw6zY0jEumv

[strong kestrel]

he's pretty good

thanks for the suggestion!

[restive gorge]

good luck

with your calc exam

[strong kestrel]

thanks man

hope you have a great day

[restive gorge]

you too

[obtuse pebble]

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[obtuse pebble]

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[rich dust]

hello

[rich dust]

i need help

on epsilon delta proofs

i am very lost

i have not begun this problem

<@&286206848099549185>

[obtuse pebble]

@rich dust Has your question been resolved?

[rich dust]

someone pls help me

[rich dust]

<@&286206848099549185> someone pls

[obtuse pebble]

@rich dust Has your question been resolved?

[obtuse pebble]

@rich dust Has your question been resolved?

[obtuse pebble]

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[primal moon]

can someone help me

[primal moon]

i know this is really easy, i kinda forgot if the answer would be 3 or dne(does not exist) since the points arent touching

[terse pivot]

f(3) = 3

but lim as x approaches 3 is dne

[primal moon]

so it would be does not exist

[copper bough]

yes

[prime swallow]

Yes

[terse pivot]

this is a peicewise funciton, as we approach from the left, negative values, we approach 5, as we approach from the right we approach -2, so DNE

[primal moon]

ty ty this is review and i forgot the case for these

[copper bough]

if the graph approaches different values from each side it is DNE

[terse pivot]

hehe wait until you get to multi variable with limits, im stuck on a problem right now

infinitely many ways you can approach a point

[obtuse pebble]

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[odd plover]

Yo help pls how do I solve question 21?

[copper bough]

JH bisecting WJM means WJH and JHM will be the same angle

[odd plover]

But how do I solve it???

I mean solve for x

[copper bough]

which also means 2(HJM)=WJM

since it gives you HJM and WJM you can just plug in each

2(4x-19)=2x+7

and go from there

[odd plover]

You’re very intelligent and bright

Let me try this out rq

One question

Would the x= 15/2?

[copper bough]

yes i think so

[odd plover]

Alrighty

Thanks bud

🫡

.close

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[vale vapor]

i don’t know what to do

help me plss😢😢

[gaunt helm]

do u see any right triangles

[vale vapor]

FCB

CF=10, FB=6, BC=8

[gaunt helm]

u can find DE as well

[vale vapor]

yea

and then?

[brazen viper]

Consider DCP and CPE would be the next thing I tried

Because DP + PE = 10

So you can get two equations and two unknowns

PE and CP

[vale vapor]

then how to get CP

[brazen viper]

You have a^2 + b^2 = c^2 for Pythagorean theorem on both triangles DCP and CPE.

These are your two equations.

You know all data except for DP, PE, and CP. But you also know that DP + PE = 10

So you have:

DP^2 + CP^2 = DC^2 = 8^2 = 64
EP^2 + CP^2 = CE^2 = 6^2 = 36

DP^2 - EP^2 = 64-36 = 28
DP^2 - (DP - 10)^2 = 28

Etc

[brazen viper]

Huh TIL

[surreal forge]

it is not very well known theorem ye

[vale vapor]

thank you, ill try to finish this

.close

[obtuse pebble]

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[dusk coyote]

How many pairs of internal "parallel" diagonals does a "Rhombicosidodecahedron" have?

<@&286206848099549185>

[surreal forge]

that seems unfortunate

[obtuse pebble]

@dusk coyote Has your question been resolved?

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[spice chasm]

how do u come up with the answer

[obtuse pebble]

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[velvet sparrow]

I've watched quite a few videos explaining the Monty hall problem and I genuinely cannot seem to understand it.

To me the information that there were prior doors dosent practically change anything, at the end it's always a simple 50/50 chance, it's whether you pick one door or another, can anyone try and explain why the fact there were prior doors matters?

In the example where there are a 100 doors I understand that the first time you picked a door you had a 1% chance but that's irrelevant to the fact that you now only have two doors to choose from is it not?

[velvet sparrow]

Is there any actual proper maths to back it up?

To me it seems more psychological than statistical

[rich dust]

.reopen

how to dhtis

[obtuse pebble]

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[hollow adder]

i need help with 10th grade eu Arrays

[hollow adder]

i need to do this without a calculator

[worthy birch]

does the comma denote decimals

[hollow adder]

yes

[worthy birch]

ok

try to convert those decimals into x/10 form

or x/100

[hollow adder]

okay

alright what next

[worthy birch]

write 1.5 as 15/10

also

simplify

like 10^7/10^8 is just 10^-1

[hollow adder]

thanks

[worthy birch]

did you get it?

[hollow adder]

i got 3*10^-6 which is correct

[worthy birch]

yep

[hollow adder]

i think i have one more

[worthy birch]

alr

[hollow adder]

I dont quite get what i am supposed to do.

the sqrt of 5 is 2.236067978 and then where is it in the 1 and 0.1 unit lengths

[worthy birch]

Looks like you have to find square root of 5 and then show where it is in the number line

do you know any ways to calculate approx values of square root of any number

[obtuse pebble]

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[sterile kayak]

for positive integers m and n is the following true: $\exists m \quad \forall n \quad m<n$

[warm shale]

syecko

[sterile kayak]

this would be false yes

[shadow dagger]

yeah (as in it's false)

[sterile kayak]

because i can choose n = 1

thus there are no such positive integers m

that are less than 1

ok thank you

.close

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[wise sluice]

theres a relative extrema around this interval

how do i solve for this?

should i do derivative test

[restive gorge]

Do y' = 0

[obtuse pebble]

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[waxen swan]

hi, does anyone know how to use the TI-84 Plus CE Python Calculator? I have a question about normal distribution

[waxen swan]

I'll just ask it first:

for the normalcdf function

when entering lower and upper limits, how do I factor in <= or >=

because for P(a<X<b) you use normalcdf(a,b,mean,standard deviation)

so I'm confused how to add "=" into the limits

But in here it just ignores the “=“

[obtuse pebble]

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[restive gorge]

you cooked

[scenic lake]

How did I get the wrong answer when I kept u and changed the limits? Only got the question correct when I subbed x^2+1 back in

[restive gorge]

Your upper bound is not 9

it's still 5

2²+1=4+1=5

[scenic lake]

Oh I’m a little special. I must’ve thought 1+4 in my head and wrote 5 instead of 1

[restive gorge]

yep

[scenic lake]

This is why I should probably use a calculator for everything lol

[restive gorge]

no

[scenic lake]

Thank you bacc!

[restive gorge]

haha

no problem Rujee

[scenic lake]

.close

[obtuse pebble]

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[uneven otter]

I dont fully understand the lipschitz continuity mathematical definition $|f(x_1) - f(x_2)| \leq L|x_1 - x_2|$. This is what I understood so far:

If the function doesnt change too quickly (small changes in the input => small changes in the output) then the function is lipschitz continuous. What I dont understand is since L isnt bounded how do I tell if L is too big or if L is too small.

[warm shale]

Calc III Victim (Pt. 2)

[uneven otter]

brah

[icy wren]

ah shoot m

sry

i delete

[uneven otter]

all good lmao

[tardy epoch]

too big or too small for what

[uneven otter]

the maximum rate at which the function can change

the lipschitz constant

[tardy epoch]

that's gonna change depending on the inputs x1 and x2

[uneven otter]

I still dont understand

[tardy epoch]

the lipschitz constant depends on the function

[uneven otter]

Say for some function if we took two inputs x_1, x_2 that resulted in

|f(x1) - f(x2)| <= 50|x1 - x2|

how would I tell

[tardy epoch]

did you read this?

[uneven otter]

I didnt really understand mb

[tardy epoch]

depends on the function mean you need to give the function to find the lipschitz constant

[uneven otter]

so something like f(x) = 100x wouldnt be lipschitz continous?

[tardy epoch]

wot

all differentiable functions are lipschitz continuous, at least locally

read the examples https://en.wikipedia.org/wiki/Lipschitz_continuity

[uneven otter]

alr

[tardy epoch]

ah shit what i said above is wrong

[dapper sedge]

they have to be C1

[tardy epoch]

Yea C^1 is what i was thinking of. thanks

[dapper sedge]

all good mane

[zenith raft]

i’m not sure exactly what the confusion is, but do note the quantifiers here

[tardy epoch]

oh yes that's why locally is important

should also depend on X the set where the inputs come from. thanks stranger.

[zenith raft]

stranger? damn

[uneven otter]

Ah so its not a lipschitz cont function if there is no single finite constant L that could control the rate of change for the whole function?

[zenith raft]

never dming you again

[zenith raft]

sure

[uneven otter]

mhm alr Imma get back to this after class

ty

.close

[obtuse pebble]

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[calm hornet]

can anyone help with some stats

[calm hornet]

some guidance how how to even start this:

[obtuse pebble]

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[obtuse pebble]

@calm hornet Has your question been resolved?

[obtuse pebble]

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[scenic ledge]

alright so

for this

prior they had added one in order to make a perfect square

what confuses me is

[scenic ledge]

in the ending they removed it

they removed the power of 2

isolating X

and solving for ONLY x alone

[scenic ledge]

i am assuming that this is indeed the root i.e. zero

and that by solving for that you would get the answer

so what im guessing is they

then use that root and put it into the original equation

and that what this is saying

is that you dont need any of the other X

if you can manage to remove them and just solve for one X that is fine

because you can still use that root for all of them

is this true?

well i mean this must be true as they did square it in the end

but something that doesnt make sense to me and this is probably an identity issue

is

[scenic ledge]

so yes they squared and divided the problem up

but

theres a kind of an issue in that

well

5 + 10 = x (x is 15)
5 + 10 = 15
5^2 + 10^2 = 25 + 100 = 75

this then leads me to

well the answer that

[scenic ledge]

they dont really seem equal

in the sense that if you did the sqrt to all operations the result drastically changes and trying to find a very specefic result of zero would not seemingly work since all operations would differ in result and equivalency

[scenic ledge]

mmmmmmmm... continuing attempts

if you were trying to isolate X....

[scenic ledge]

25 + 100 = 75 sqrt them for 5+10 = 15```

[scenic ledge]

well i forgot that 15 w a s X now that i think about it err

and thatit was separate

what a mess

ill make a new channel

.close

[obtuse pebble]

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[timid silo]

hi

[timid silo]

is A^2 + B^2 equals to (A+B)^2 ?

[junior granite]

generally no

[opaque dome]

Only if a or b is zero

[timid silo]

comon

[timid silo]

okay

[opaque dome]

Otherwise you have to add 2AB

[timid silo]

now i am doign some weird questions,
and getting condused between

[opaque dome]

To get it

[timid silo]

a^2-b^2
and (a-b)^2

can you guys explain

[opaque dome]

Same only if a or b is zero

[timid silo]

it is not allowed to do something like that lol?

[opaque dome]

Heresy

xd

[timid silo]

no, i am not saying those are equal or anything but, what i am trying to say is, how do i understand which one to use

[opaque dome]

!original

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[opaque dome]

It depends the context for sure

[timid silo]

i am solving some inverse trigo ques

the question is totally unrelated

i am not able to get the idea of which one to use

i faced this issue in calculus as well

probably some learning gap

[opaque dome]

But it just depends on how its written

[timid silo]

yeah that's what i am asking

[opaque dome]

And we can't help you since we don't see how its written

Like if you have (a+b)^2 = a^2 + b^2 + 2ab

But if you have a^2 + b^2, theres a specific but useless one identity

Involving the one above

[timid silo]

tell?

[timid silo]

that i know

okay

how about this

(a+b) * (a-b)

can i call this (a-b)^2

[opaque dome]

a^2 + b^2 = (a+b)^2 /2 + (a-b)^2 / 2

[opaque dome]

No

Develop both and see

(a-b)^2 = a^2 + b^2 -2ab

[timid silo]

yeah we are getting extra 2 ab

[pallid orbit]

1+1=2

[timid silo]

a^2 - b^2 it is then

[opaque dome]

For the other one

So you have 2ab in more and a b^2 changing sign

[timid silo]

yup

[opaque dome]

Stop

[pallid orbit]

ok

[timid silo]

bro, im not sure how your parents handle you

i might lose it if it was me

lol

[pallid orbit]

lol

[timid silo]

actually, that shit makes sense now, i need a break

[opaque dome]

Fine, have a good break then

[timid silo]

making basic mistakes

literally one fucking sign

rip

[timid silo]

thx, you too

hi

guys wait

one last thing

[pallid orbit]

ngl I am so bad at math

[opaque dome]

Yes

[timid silo]

sqrt a+b * sqrt a-b

[pallid orbit]

bruh

[timid silo]

what will that bcome

become

[timid silo]

i wanna finish this lol

[opaque dome]

Nothing to do further with this

[pallid orbit]

lol

[opaque dome]

Oh wait

[timid silo]

yes this can be simplifed

[opaque dome]

Yes

It can

Only if a>b

[pallid orbit]

what does this mean?

😭

[timid silo]

not really, who told you that?

in some cases my b will be lower than a

something like this it will be

yeah

i got it

thanks everyone

i am an idiot

[opaque dome]

So you will have to treat it different way

[pallid orbit]

My 13 year old brain might just die 💀

[timid silo]

lol

nah it is easy stuff

[pallid orbit]

EASY????

[timid silo]

nope we don't have to, what makes you think we have to?

[pallid orbit]

😭

I aint readdy for highschool

[timid silo]

yeah, soon you will learn it too buddy

[opaque dome]

Ohterwise negative sqrt

[timid silo]

hmm

[pallid orbit]

ok because I just joined today 💀

[timid silo]

good point

[opaque dome]

And multiplicity doesnt apply to negative

[timid silo]

yeahhhhh

good point

[opaque dome]

Thats why

[timid silo]

hahahah, you are looking for firends here? lmao

ask some maths questions here

[pallid orbit]

If there is a black hole then should there be a white hole to?

[timid silo]

didn't notice

yup

[pallid orbit]

IDK 😭 I want to get smarter

[timid silo]

okay, do not ever ask questions again.

thank you

[pallid orbit]

bruh

ok

[timid silo]

hahaha jk

[pallid orbit]

alr

lol

how old is the water in my body

2 million years old?

idk

[feral ember]

hi guys

its me

alvin

[pallid orbit]

hello spider

[feral ember]

from alvin and the chimpmunks

[pallid orbit]

💀

[feral ember]

@timid silo

whats 20 devided by 37.9 squared

[pallid orbit]

tbh

I have no clue

im not liein

[feral ember]

ima leave

give me a reason to saty

[pallid orbit]

your spider

there for you should stay

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

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

[dawn falcon]

1

[hidden compass]

If you had to find the vertical asymptotes of that function, how would you do it?

[dawn falcon]

u set the denominator to = 0 ?

but arent the asymptotes already given to me

oh wait i got it

.close

[obtuse pebble]

Channel closed

Closed by @dawn falcon

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[obtuse pebble]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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[naive kindle]

max(0,x) can someoen explain how this is equivalent to the relu

[naive kindle]

how would i read this

[tardy epoch]

what's the definition of relu

[naive kindle]

piecewise function, if x is neg its cut at 0

otherwise x

[radiant oxide]

who here knows their combinatorics very well

[wary badger]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[radiant oxide]

oh sorry

[naive kindle]

$$\text{ReLU}[x]=\begin{cases}
0 ~~~~~~\text{if }x<0
\
x ~~~~~~\text{if }x\geq0
\end{cases}$$

[warm shale]

pyrate

[wary badger]

if x<0 then the max(0,x) is 0

because 0>any negative number

[zenith raft]

it is the exact same thing as max(0,x)

oh

[wary badger]

if x>0 then max(0,x) is just x

[zenith raft]

you asked why

[naive kindle]

yee im just trying to understand the notation

[wary badger]

since x is positive it’s going to be greater than zero

[zenith raft]

🥩

[wary badger]

🥩

[naive kindle]

so for the max function, you pass x in and it compares the two (0 and x)

and returns whichever is max

or greater

[tardy epoch]

indeed

[naive kindle]

kk cool

ty

[zenith raft]

so many s

[naive kindle]

indeed

.close

[obtuse pebble]

Channel closed

Closed by @naive kindle

Use .reopen if this was a mistake.

[tardy epoch]

could be more if you changed your username

[zenith raft]

it would be less

[tardy epoch]

[zenith raft]

[obtuse pebble]

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[shrewd comet]

help check if correct

[unreal musk]

You didn't quotient rule right here

[shrewd comet]

ok wait

[unreal musk]

Yep

Then of course, you can (re)do the tangent and normal gradient from there just multiply them both by -1, cause that's the only difference between them

[shrewd comet]

so grad tangent is pos

grad normal is -2/3

[unreal musk]

Yep, which visually matches up, as per yesterday's comment

The normal is going down so should have negative gradient, the function at P is increasing so should have positive gradient there

[shrewd comet]

ok so eqn would be y=-2/3x +4/3

how to start

[unreal musk]

It seems they want you to do this one by working out the area under the curve, so this blue area, first - do you know how to find that?

The area under y = 8/(1 - 3x) and above the x axis between x = -1 and x = 0

[shrewd comet]

erm no what formula should i use

[unreal musk]

Yep, that gets you the area do you know how to integrate 1/x?

(this one is a little bit special )

[shrewd comet]

lnx

[unreal musk]

Yep, though keep absolute values just in case, ln|x|

So you can work out that integral $\int_{-1}^0 \frac8{1 - 3x} \dd x$ fine?

[warm shale]

@unreal musk

[unreal musk]

You just need to work out that $-\frac83 \ln\abs{1 - 3x}$ between the limits of 0 and -1 now! (you don't need a $+c$ for definite integrals, they'll cancel out anyway!)

[warm shale]

@unreal musk

[shrewd comet]

oh ok

[unreal musk]

The limits are 0 and -1, aren't they?

[shrewd comet]

oh shoot

where did i get that

[unreal musk]

Happens sometimes

[unreal musk]

Number seems about right you don't need the outer absolute value bars here, and the line above it is 0 + (8/3)ln(4) anyway

[unreal musk]

Anyways, once you found that, they want you to get the area of this trapezium, the area under that normal (with equation here!) between x = -1 and x = 0

Hopefully that's easier to find

[unreal musk]

There you go well done

[shrewd comet]

thanks!!! last qn hehe

how to start

do i just equate the LHS to the A earlier

[unreal musk]

Basically they've already given you the start of the question, you're starting off with this, the integral on the right representing that area B

Just work the integral out and find out what the bottom limit needs to be

[shrewd comet]

not this?

oh wait i didnt see the x

on the integral

[unreal musk]

,rccw

[shrewd comet]

how do i get the Q

[unreal musk]

The x coordinate of Q is the value for x you'll find when you work the integral out

[shrewd comet]

erm

[unreal musk]

Yep

Then expand both sides, that should be nice to solve, $\frac83 \ln(4) = \frac83 \ln(4) - \frac83 \ln(1 - 3x)$ (the absolute values removed because $1 - 3x$ would be positive when $x < -1$)

[warm shale]

@unreal musk

[shrewd comet]

huh

what do u mean expand

[unreal musk]

Distribute that 8/3 to all terms here

[shrewd comet]

isnt it already the 2nd line

[unreal musk]

Oh yeah, so it is then just simplify the insides of the log and don't factor it

[unreal musk]

Yep

[shrewd comet]

erm whats after

[unreal musk]

And that's all equal to $\frac83 \ln(4)$, that is:
[
\frac83 \ln(4) = -\frac83 \ln(4) + \frac83\ln(1 - 3x)
]

[warm shale]

@unreal musk

[unreal musk]

So solve that for x

[shrewd comet]

eh how

u said we dont factor

[unreal musk]

Don't factor the right hand side it makes it easier to move stuff around now to get the stuff that has x in it by itself!

[shrewd comet]

i dont get it

[unreal musk]

Alright, let me give you a new question: do you know how to solve the equation 59 = 69 + 4u, for the variable u?

[shrewd comet]

oh we're able to transpose?

i thought we need to prove LHS=RHS lol

[unreal musk]

Noooo you're just solving an equation here, rather than proving they're equal

[unreal musk]

,rccw

[unreal musk]

Yep you take the x = -5 one here of course, because if you look at the graph, you "clearly" want x to be less than -1

[shrewd comet]

got it

what about the next line?

its the same

[unreal musk]

Oh I wonder why they even gave that to you, they really tried to make your life so easy

You can ignore that cause you ended up with that before anyway

(also ping replies please just in case I don't see them )

[obtuse pebble]

@shrewd comet Has your question been resolved?

[obtuse pebble]

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[tulip zodiac]

Hello, I was trying to solve the birthday problem, and my intuition was: Since we want to find the probability of at least one match, then I could find the probability of each pair of people P(A intercept B) = 365/(365*365) multiplied by nCr(n, 2) minus all the times the interception has been taken into account which would be (n-1) (365/365^n) so the whole formula would be

but this doesn't match with the results ive seen online

[obtuse pebble]

@tulip zodiac Has your question been resolved?

[obtuse pebble]

@tulip zodiac Has your question been resolved?

[obtuse pebble]

@tulip zodiac Has your question been resolved?

[tulip zodiac]

Update: I have been using this formula because I noticed some flaws in my train of thought

for n = 4:
$\operatorname{nCr}\left(4,2\right)\cdot365\cdot\frac{364\cdot363}{365^{4}}+\operatorname{nCr}\left(4,3\right)\cdot365\cdot\frac{364}{365^{4}}+\frac{365}{365^{4}}$

[warm shale]

Edsel Di Meo

[tulip zodiac]

This almost matches the calculation
$1-\frac{\left(365\cdot364\cdot363\cdot362\right)}{365^{4}}$

[warm shale]

Edsel Di Meo

[tulip zodiac]

There's some combination I'm not taking into account in my formulation

but they are reaaaaally close

My formula yields 0.01633345586 the correct one 0.01635591247

for n = 5, it's the same thing

my formula: 0.02702411102 the correct one 0.0271355737

[obtuse pebble]

@tulip zodiac Has your question been resolved?

[obtuse pebble]

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[crude cape]

How can i simplfy this expresion?

[obtuse pebble]

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[crude cape]

How can i simplify this expresion? or i cant simplify this more

[obtuse pebble]

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[last pilot]

what exactly is your question @timid silo

[timid silo]

I don't get the formula

[last pilot]

for derivatives?

[boreal cliff]

It's not readable either

not for me at least

[last pilot]

i can

[timid silo]

I dont understand

[last pilot]

okay

so the top

i.e. f(n + delta n) - f(n)

is simply the change that occurs in f(x)

when you change x by delta n

and delta n is simply the change in x

so this is really just (change in y)/(change in x)

aka slope

it's just that we add a limit

to get instantaneous slope

[timid silo]

Slope means

[last pilot]

...

[boreal cliff]

...

[last pilot]

like the rate of change of the graph

the rate at which it curves, you could say

[boreal cliff]

$\frac{\text{Rise}}{\text{Run}}$?

[warm shale]

Percy

[amber snow]

tangent ryt

[boreal cliff]

not me latexing that for no reason

[boreal cliff]

no a tangent is a line

[last pilot]

^

let's forget tangents

that'll confuse OP

[boreal cliff]

yes

[amber snow]

rise/run = tanx = slope
i mean am i right

[last pilot]

this is slope @timid silo

[boreal cliff]

if you're british, it's gradient

we mean gradient

[last pilot]

...
again, don't go off topic here

and no not always

i think op is indian

[timid silo]

Rise and run !?

[iron edge]

How steep a slope is

[last pilot]

yes...?

how steeply the graph curves

[boreal cliff]

I don't wanna be assuming stuff but I sus that too lmao

[amber snow]

negativen't

[boreal cliff]

op are you indian and if so in what class

[last pilot]

what...?
dude stay on top please

[amber snow]

11 rn

[last pilot]

main hindi bol sakta hu agar aapko vo aur aache se samaj aayega

[last pilot]

you aren't OP... @timid silo is

;-;

[timid silo]

So confusion

[boreal cliff]

bro thinks he's op ;-;

[last pilot]

what?

[amber snow]

thought you were talking about my post lol

[boreal cliff]

@timid silo

[timid silo]

Op ??

[boreal cliff]

original poster.

[last pilot]

*sighs*

[timid silo]

Yoss

[last pilot]

oh ok

[amber snow]

mere hindi bhot bakhwaas h

[boreal cliff]

what class

[obtuse pebble]

Please read the channel description before posting, and stay on topic.

[last pilot]

@amber snow

[timid silo]

Class 11

[boreal cliff]

...the 'm' in y=mx+b is the slope?

ykwim

except here it need not be a line.

[last pilot]

^

[boreal cliff]

just the rise over the run

[timid silo]

😭 that's new for me i ma weak in maths but i get ur point 🤧

[boreal cliff]

you're an indian in 11th grade

[last pilot]

okay percy

[boreal cliff]

dhikkar /lh

[last pilot]

no stereotyping

i see where you're going with this

[boreal cliff]

im joking obvs

[last pilot]

that's perfectly fine, we're here to help

[timid silo]

I ma from nepal

[boreal cliff]

ah

[timid silo]

Thx 😢🥹

[last pilot]

do you understand the basic concept of slope

[timid silo]

Noi 🤧

[last pilot]

okay

slope is basically how steep a graph is

if a graph has very high slope

that means the "y" of the graph increases very quickly

if you increase the x only a little

if a graph has low slope that means that the graph's y value changes slowly in comparision

a graph with 0 slope is a flat graph--the y doesn't change; it's a constant graph

and a graph with negative slope decreases with increases in x

[timid silo]

Oh ok ty i understand some point

[last pilot]

good

i suggest you get a bit comfortable with slope

before you do derivatives

because derivatives really require you to fully understand slope

[timid silo]

Can u teach me slope

[last pilot]

https://www.youtube.com/watch?v=jvjZ4rnERmM&ab_channel=TheOrganicChemistryTutor

tbh im not a very good teacher

this guy is tho

[iron edge]

I was about to send this 🤣

[last pilot]

watch it and lmk if you need help

[last pilot]

lol sniped

[timid silo]

Tysm 😭🥹

[last pilot]

no worries lol

[timid silo]

Yepp 😭

[last pilot]

did you watch it?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[lone bobcat]

What am I doing wrong?

[obtuse pebble]

@lone bobcat Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[lament iron]

Honestly no idea what this even means? Big ask but can someone help my explain this as I don't even know what to search up to learn this?

[lament iron]

like I vaguely understand what one-to-one/onto mean, what a modulus is but as a whole idk

[solar meadow]

It said here that M(x) is a function such that if x is an integer, M(x) is also an integer

[vale pelican]

M is an integer-valued function, taking an integer x and computing the remainder of (2x+5)/7

a function is called one-to-one (injective) if every input corresponds to a unique output, i.e. M(x) = M(y) implies that x = y

[solar meadow]

(2x + 5) (mod 7) is the remainder when 2x + 5 is divided by 7 (Number Theory).

[vale pelican]

a function is onto (surjective) if for every element z in the codomain, there is some x in the domain for which M(x) = z

to show that M is indeed a function, it must provide only one output for each input, i.e. if x = y, then M(x) = M(y)

[solar meadow]

But Since (2x + 5) (mod 7) belongs to {0, 1, 2, 3, 4, 5, 6}, It is not a one to one function.

[vale pelican]

I know

[solar meadow]

I was explaining it to her.

[vale pelican]

well I thought about that afterward but still we don't need to jump ahead lol

[lament iron]

ok so it's the domain stuff that's confusing me rn

m(x) is a function that calculates the modulus of the sum (2x+5)?

[vale pelican]

mod 7, yeah

[solar meadow]

Yes.

[lament iron]

errr

and there's a certain amount of ouputs that map to something?

[vale pelican]

the outputs are what's being mapped to

inputs map to outputs

[solar meadow]

There's only 7 available outputs and there are infinitely many integer inputs

[lament iron]

right right I think I'm getting it

so there's 2 "fields", inputs and outputs? and each input maps to a certain output?

[vale pelican]

yeah

[lament iron]

and I assume I'm trying to prove that that there's a limited amount of outputs?

[vale pelican]

inputs live in the domain, outputs live in the codomain, and the function maps each input to one output

[lament iron]

okok

[vale pelican]

that's a large part of it, yes

[solar meadow]

Do you know why there is only a limited amount of outputs?

[lament iron]

I would assume since there's only a limited amount of answers the mod can be

0-6?

[lament iron]

so I assume I'd be sayign something to that effect, that there's a limited codomain and infinite domain?

then I'm just trying to prove that it's either one-to-one or onto? or are those different things

[vale pelican]

they are different things

1-to-1 says that each output is reached at most once

whereas onto says that each output is reached at least once

[lament iron]

aaah

[vale pelican]

actually I don't mean "output" here

I mean each element in the codomain really

so each codomain element is an output for at most one / at least one input, respectively

[lament iron]

ok right I think I got it

so would I not just assume that it's onto? given there's an infinite domain?

how would I figure that out?

[vale pelican]

the useful definitions are here and below

M is onto if for every z in the codomain, there is some x in the domain for which M(x) = z

in this context, for every integer z, there is an integer x so that M(x) = (2x + 5) mod 7 = z

and you must determine if this is true or false

[lament iron]

riiiight I think?

uhhfgjhjkf

ok I think I understand conceptually at least, but idk how I'd do that mathematically

my first instinct of understanding is that I'd solve for x = 1 in the original formula or something, then find the output?

then like throw both the input and output into those formulas or something?

[solar meadow]

1: 7 inputs has to have 7 unique outputs
2: 8 inputs has to have 8 unique outputs|
3: infinity > 8
4: take out any 8 inputs from the infinitely many integer inputs
5: Notice you need 8 outputs but you only have 7
6: QED

[lament iron]

right I understand that. but how should I demonstrate that? do I literally just type something to that effect? Do I manually test the case for 8 inputs? or is that something I'm demonstrating with the formulas above?

[solar meadow]

Just prove it logically with the statements

1. 7 inputs has to have 7 unique outputs
2. 8 inputs has to have 8 unique outputs
3. infinity > 8

[lament iron]

okok gotcha

[rocky goblet]

i mean tbh what i'd do here is just

"onto" means for each element of the codomain, there's some element of the domain that gets mapped there

so to show it's not onto, find some element of the codomain, and show that no element of the domain is mapped there

we know that the only possible outputs are 0, 1, 2, 3, 4, 5, 6, so you can just give like, 7, as an example, and prove that M(x) can never be 7

and then that implies M isn't onto

[solar meadow]

???

[lament iron]

Alright this is what I've written as my answer:

As the function m(x) = (2x + 5) mod 7 always returns values between the set (0, 1, 2, 3, 4, 5, 6) we know that there’s a limited codomain.

We can also understand that there’s an infinite domain, as the input, x, is not restricted.

Logically, one-to-one demonstrates that for each element of the codomain it matches to exactly one element of the domain. Automatically, we can understand that M is not one-to-one, as there’s far greater elements in the domain than elements in the codomain. This mean that M is onto.

Would this work?

[rocky goblet]

...well that's valid if you've proven all of the facts about cardinality that you're implicitly invoking there, although my way does actually seem like a shorter proof and also follows directly from the definitions

[rocky goblet]

also you're getting confused here between "range" and "codomain"

they said M : Z -> Z, so the codomain is Z

the set of outputs that the function actually has, which in this case is {0, 1, 2, 3, 4, 5, 6}, is called... ok well i call it "range", but according to wikipedia people sometimes use that to mean the codomain, and the people who do that instead call it the "image", which i use to mean something else, ok so basically the terminology is a mess actually

but it's definitely a different thing

[lament iron]

lmao

[rocky goblet]

by your logic here all functions would be onto

[lament iron]

hmmm

[rocky goblet]

but the fact that its range (or whatever we're calling it), {0, 1, 2, 3, 4, 5, 6}, isn't the same as its codomain, Z, ...is just what it means for it to not be onto, so

[lament iron]

so my assumption is that there's 2 seperate things, codomain and range? but in this scenario they both just have the same values?

and you're saying I can't equivocate them?? or something?

I'm kinda lost

[rocky goblet]

no in this case they're completely different

one is {0, 1, 2, 3, 4, 5, 6} and the other is Z

[lament iron]

sooo

[rocky goblet]

"M : Z -> Z" means its domain and codomain are both Z

a function is onto iff its range is equal to its codomain

[lament iron]

aah right ok

[rocky goblet]

the range of this particular function is {0, 1, 2, 3, 4, 5, 6}, which is not Z, therefore it's not onto

[lament iron]

nvm i'm lost lol

so you're saying it's not onto?

[rocky goblet]

yes

[lament iron]

but it can't be one-to-one either?

logically one-to-one is that one element map to another, but with infinite inputs and finite outputs, that can't be possible?

[rocky goblet]

yep, it's not one-to-one either

(i don't know why you're specifying "logically" here)

for instance M(0) = M(7)

wait it's called M why did they call it M

[lament iron]

I say logically, cause that's how my brain is doing it logically, I literally have only learnt of these concepts 30 mins ago lol, I could be entirely wrong :P

but regardless, doesn't it have to be one of the two?

the question itself states onto OR one-to-one

[rocky goblet]

...no

[round rock]

A function in general doesn't have to be either even if the question implies it is

[rocky goblet]

as an even simpler example, the function f : Z -> Z defined as f(x) = 0 is not one-to-one and is not onto

it sends everything to one value, so it's not one-to-one, and it doesn't send anything to any of the other integers, so it's not onto either

and yeah the phrasing of the question is maybe not ideal but they just meant it as two separate questions

1. is it one-to-one
2. is it onto

[lament iron]

yeah true I guess

it says "determine IF IT IS one-to-one or onto"

mb

so how do I actually go about solving this then

[rocky goblet]

...well we just did?

it's not onto, because it can only ever output values in {0, 1, 2, 3, 4, 5, 6}, which isn't all of Z

it's not one-to-one, because M(0) = M(7) but 0 is not 7

[lament iron]

suuuuure ⁉️

[lament iron]

and it's not all of z because z also had to include all the inputs given M: Z > Z?

[rocky goblet]

...no, i have no idea what you're talking about

i meant that {0, 1, 2, 3, 4, 5, 6} and Z are different sets

[lament iron]

https://cdn.discordapp.com/attachments/198793672119156737/1275514671272693845/ezgif-5-0360d2c3e3.gif

[rocky goblet]

for instance 7 is in Z, but it is not in {0, 1, 2, 3, 4, 5, 6}

also 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc., are all in Z and are not in {0, 1, 2, 3, 4, 5, 6}

so they're different

[lament iron]

and I'm tryna ask what z is

[rocky goblet]

it's the set of all integers

[lament iron]

wha

[rocky goblet]

...if you didn't know that then that explains a lot of why you've been finding this confusing

[lament iron]

ok now sure maybe I get it

[rocky goblet]

$\mathbb{Z}$

[warm shale]

bee [it/its]

[round rock]

Iconic symbol

[lament iron]

yah

like I said I've never learnt of any of this stuff till now, I just assumed z was standard notation for domain/codomain, like x or y, like I originally thought that I was trying to find the (co)domain and that's what the (0, 1, 2, 3, 4, 5, 6) was

or i,j, k

[round rock]

Imagine X & Y in this picture are both Z

[lament iron]

yeah yeah

[round rock]

And f(x) is your M(x)

The picture would have an infinite amount of dots pointing in the red section to the yellow section (ie, many to one)

And no dots in the red pointing to anything in the blue (not all onto)

[lament iron]

as in the yellow section would be in the red section?

[round rock]

No, the yellow section represents the set {0,1,2,3,4,5,6}

[lament iron]

https://media.discordapp.net/attachments/844678220837814282/1269767155180896359/cat-fire-ezgif.com-video-to-gif-converter.gif

I gotta drop out bro

uhhhhhhghgsdkfk

alright I think I vaguely understand

[round rock]

Red section is Z and blue section is also Z

Yellow section is inside the blue section bc {0,1,2,3,4,5,6} is a subset of Z

[lament iron]

sure

 As the function m(x) = (2x + 5) mod 7 always returns values between the range (0, 1, 2, 3, 4, 5, 6).

We can also understand that there’s an infinite domain as the input, x, is not restricted. And as M: Z > Z, we understand that there’s also an infinite codomain.

Logically, one-to-one demonstrates that for each element of the codomain it matches to exactly one element of the domain. Automatically, we can understand that M is not one-to-one, as there the set of answers is only 7. However, it’s also not onto as not every codomain is in use either, as the set of answers is far smaller than the codomain.

Revising my previous asnwer, does this sound vaguely correct

ignoring my incomplete sentences

smh

[round rock]

Adding examples for your reasoning would be good too

[lament iron]

but it's vaguely correct?

[round rock]

 However, it’s also not onto as not every codomain is in use either,

"not every element in the codomain is in the range"

[lament iron]

aah that would prob be better wording yeah

[round rock]

Domains and codomains are usually defined depending on what type of numbers you are "playing with"

In this case all the numbers we are using are integers which is why they both Z

If I were to make a function that turns an integer into decimal then it would be like f: Z -> Q

And what's Q?

[lament iron]

uh

uhh

irrational numbers ⁉️

or rational numbers ⁉️

[round rock]

Yeah so you need to learn your definitions for sets of numbers

[lament iron]

I only remember R cause Real numbers

[round rock]

it's rational aka quotients (hence the Q)

[lament iron]

ah gotcha

[round rock]

You'll be seeing them a lot so it's good to remember

[lament iron]

yeah nah I learnt that stuff like 3 years ago in late high school lol

[round rock]

Well good is an understatement, it's necessary

[lament iron]

right

[round rock]

Yeah sometimes things you think aren't helpful pop up years later

[lament iron]

real asf

doing computer science and didn't realize how much math was involved

[round rock]

I did computer science and switched to maths actually haha

Preferred the maths side of it

[lament iron]

that's kinda real tbh

learning maths beats my ass but once I've learnt it or just learning certain fields in general are really interesting to me

coding/network side is boring asf though :(

took a coding class and hated it in high school but I just thought it was cause the teacher sucked </3

BUT REGARDLESS

Thanks for the help the four of you :3

.close

[obtuse pebble]

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Use .reopen if this was a mistake.

[obtuse pebble]

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[idle plume]

calc 3 book problem

i cant figure out how to find the limit of the sequence

[median dome]

so we wish to find $\lim_{n\to\infty}\sqrt[n]{5^n+3^n}$

[warm shale]

kheerii

[median dome]

first what do you feel like the limit should be?

[idle plume]

well i kinda cheated and checked the graph 😭

its 3 or 5