help-36

[steady wraith]

woah

that's still pretty good

[late bolt]

Well you'd save yourself the exam fees

[steady wraith]

wait so were you applying for maths?

[late bolt]

Yup

I mean it's alright I'll just be going imperial instead

[steady wraith]

if i go to cambridge though I'd save myself the fees in london like 3 of my other uni options

[steady wraith]

damn

[late bolt]

Well the london loans are bigger too tbf

[steady wraith]

wait so you did TMUA?

[late bolt]

Yeah

[steady wraith]

wait what did you get

on tmua

because I am also applying for cambridge and imperial

[late bolt]

Not as well as I'd like but good enough apparently

I'm lowk pissed off about it

[steady wraith]

7?

[late bolt]

I had gotten as high as 8.9 when doing past papers

[steady wraith]

tbf "good enough" probably depends on your predictions

[late bolt]

Only to choke and get 6.2 on the real thing

[steady wraith]

oh

[late bolt]

Lowk I blame those pearson test centres

[steady wraith]

shit im not doing that good on the past papers

I'm getting 7.5

[late bolt]

I had 3 x A* and 1 x A predicted

[steady wraith]

yeah that's probably why

[late bolt]

A* in maths fm and physics, A in chem

[steady wraith]

I have 2 x A* and 1 x A predicted

[late bolt]

You'll be golden with that score dw

[steady wraith]

my cs teacher isn't letting me get an A* predicted despite being less than 3% off the grade boundary for it

😭

[late bolt]

Well that's the standard offer isn't it? U should be fine

[steady wraith]

true but the room for error is probably narrower

[late bolt]

Damn, my chem teacher was similar

[steady wraith]

like I'd need stronger interview performance for cambridge

than the average applicant

and probably stronger TMUA results too

[late bolt]

Well tbh I thought my interview went terrible

[steady wraith]

also again, that's if I get it

[late bolt]

I mean it didn't go fantastic as I was pooled but still it mustve went good enough

[steady wraith]

ig everyone does

[late bolt]

Basically what I'm saying is

Everyone thinks the interviewer expects u to be the next Terrence Tao

But it's not usually like that

[steady wraith]

true

idk how to perform "above average" then

[late bolt]

Even if u fumble through the question, just explain ur thoughts and they might pick up on how clever u actually are in a non-interview setting or smth

[steady wraith]

if it's not about making as little mistakes

[late bolt]

They just want abstract thinking ibr

[steady wraith]

oh yeah true

don't they only offer to 20-30% of people they interview

[late bolt]

Ermmm I'm not sure tbh

What I do know is that they give out 2x as many maths offers as they have

[steady wraith]

ik

[late bolt]

And chop half based on step

[steady wraith]

the thing is tho if you do well on step

then you're guaranteed a place

if you get 1,1 or higher

even with 1,2 they sometimes let you off

since they apparently check your working

[late bolt]

Yeah I know a guy who got 1-2

They pooled him to a dif college but he still made it

[steady wraith]

so if you lost marks due to silly mistakes or something but had the understanding

[steady wraith]

yeah

I guess tbh though

[late bolt]

So what they do with the 1-2s and the 2-1s

Is they ask for ur FM marks breakdown

[steady wraith]

i don't know a single person with only 2 A*s predicted who got a cambridge or even imperial offer

so like

idk

[late bolt]

And assess u w/ the other 2-1s and 1-2s

[late bolt]

Hm idk

[steady wraith]

oh so when that happens they take your a level fm scores

[late bolt]

Yeah apparently

[steady wraith]

and use that too

then

ah

[late bolt]

Or at least they did for this guy

[steady wraith]

i mean fe

idk how you can not do well in fm but do well on step ii/iii

[late bolt]

I mean I'm sure they give offers to ppl predicted 2 A* since it still meets their standard offer

[steady wraith]

because step ii/iii requires fm proficiency anyways

[steady wraith]

yeah true

it's just idk concerning

[late bolt]

You'd be surprised actually

[steady wraith]

that it seems rare

[late bolt]

What can happen is STEP demands more revision time

And FM gets a bit neglected sometimes

[steady wraith]

oh yeah true

that's what happened when my original choice was oxford

[late bolt]

I have heard of one instance where someone got 1-1 in STEP and A in FM

[steady wraith]

I neglected FM for MAT

[late bolt]

Ngl ur a masochist bro

[steady wraith]

and sure i was getting like 70-90% in MAT mcqs but like

[late bolt]

TMUA, MAT, and STEP??

[steady wraith]

my fm scores were BAD

[late bolt]

Insane

[steady wraith]

i dropped oxford

for cambridge

because again

neglected fm

[late bolt]

Fairs

[steady wraith]

and also i feel my chances are decently lower in oxford than camb

[late bolt]

I'd disagree tbh

[steady wraith]

wait just curious what did you acc get in STEP

[late bolt]

MAT is far easier

[late bolt]

2-2

[steady wraith]

yea true but oxf has less places and they filter out applicants earlier

[steady wraith]

ah ok

ig that's not too bad

[late bolt]

Yeah not good enough for cambridge

[steady wraith]

yeah true

ik someone who used to be in my school who got 1,1 in STEP

and is now at oxford

[late bolt]

Well anyways at least I can flex that I got an offer in the first place so not all is lost

[steady wraith]

so he's marking any step papers i do

[steady wraith]

yea

i mean i doubt i'd get that far

tbh

[late bolt]

Oh nice

[steady wraith]

with my predictions/gcses

[late bolt]

You'll be fine

What kind of background we looking at?

No need to answer if its too invasive

[steady wraith]

i have extenuating circumstances (major depression) during gcses but I also go to a grammar school and pretty much most of the people i know got mostly 9s

I got mostly 7s and 8s

with one single 9

[late bolt]

Well yk all offers they make are in the context of ur situation so

[steady wraith]

with the extenuating circumstances tho i think im still in the running

[steady wraith]

ye

[late bolt]

I wouldn't worry too much about the gcse grades

[steady wraith]

still i think for me they'd weigh interviews a bit higher

[late bolt]

or the predictions tbh

[steady wraith]

than most other people

[late bolt]

Plus u have the bonus of not being from a private school

[steady wraith]

true

[late bolt]

If it helps I also got mostly 8s and 7s in my gcses

[steady wraith]

oh wait really

ok

i'm calm then

[late bolt]

I think I had 3 9s, 2 7s, and the rest 8s

[steady wraith]

that's mostly 8s and 9s

not 7s

but uh

ok

[late bolt]

And then a few odd ones like A, distinctions

[steady wraith]

i got 4 7s

[steady wraith]

ah i didnt do fsmq

still

nice

[late bolt]

Oh wait yeah good point I guess my perception was a bit twisted

It's late ignore me 😭

[steady wraith]

oh dw

[late bolt]

Did u do gcse FM then?

[steady wraith]

wait did you apply for maths or was it cs or another stem

[steady wraith]

yeah

[late bolt]

Maths

[steady wraith]

i got a 7 in FM

😭

[steady wraith]

oh ok

yeah im doing maths for a bsc too

then cs for a msc

[late bolt]

Hey thats still solid

extenuating circumstances remember?

[steady wraith]

yea true

[late bolt]

Oh niceee

I acc rly wanna get into some programming related maths but I didn't do CS A level

Anyways I enrolled for MSci maths even tho I'm not 100% sure I want a masters

[steady wraith]

you can probably try again for a msc if you have evidence of interest in cs

[steady wraith]

oh ok

[late bolt]

Just bc I have the flexibility to move down to BSc if I like

[steady wraith]

yeah nvm

[late bolt]

Whereas moving from BSc course to MSci integrated masters is trickier

[steady wraith]

I mean

[late bolt]

I could still switch up after year 3

[steady wraith]

if you get a first class or something as a BSc

acc even without a first class

cant you still do a MSc at imperial

with a bsc

it can't be that hard to move surely

[late bolt]

Idk if it would still be integrated masters tho

[steady wraith]

oh yea true

[late bolt]

I may have to give up another year

[steady wraith]

it won't be integrated

it won't be the area under the curve masters

[late bolt]

Well either way tbh my course has python modules in year 1 and more optional programming modules later on

So I'll get to dabble in programming a little if nothing else

[steady wraith]

yea true you are in a good position either way at imperial

i think just make sure you do some internships

[late bolt]

I hear they have one at MIT

But like only for the best student or smth

[steady wraith]

yeah they do

[steady wraith]

yeah

thats what i was gonna say

[late bolt]

So probs not me

But who knows

[steady wraith]

yeah

i think if i do a bsc at imperial or camb and get a first class

i'd acc try applying for mit

and us universities

[late bolt]

U wouldn't want to complete the tripos?

[steady wraith]

for a msc? idk

[late bolt]

Alan Turing did the tripos

He's probs ur goat or smth given that ur into CS and shit

[steady wraith]

i mean isnt a cs msc more useful than a maths msc to get into tech

[late bolt]

Maybe, I'm no expert on CS

Well anyways as cool as MIT is

I don't think I could go uni there

For a year sure

But I couldn't live long term in the states

[steady wraith]

yeah idk if i would either

who knows tho

[late bolt]

Plus nows not a great time to be a foreign student in america

Seems like a guarantee to get deported

[steady wraith]

yeah that's true

[final saddle]

@steady wraith Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[north spear]

was wondering in a)

we are gonna use this formula:

where we know what n is=

but is v= [ 1 0 0 , 0 1 0 , 0 0 1}?

or something else that i have missed?

[proper dagger]

!15m

[final saddle]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[north spear]

yea ik but i am rly in a hurry have the exam in a few hours ...

anyone plz? 🙂

<@&286206848099549185>

[deep condor]

i am unsure what this formula is, but v should be a vector, judging by the notation

what's the full formula?

[north spear]

yes that the formula

for planes

[deep condor]

hm

again hard to say without seeing the full formula

[north spear]

thats the formula?

[deep condor]

oh fr? weird

[north spear]

but its found in chat

but the v is x

and the n is v

[deep condor]

i only see v = (x_1, x_2, x_3) as a possibility

but if n is the normal vector of the plane, v dot n = 0

[north spear]

?

[deep condor]

oh wait sorry that's (v-a) dot n = 0

[north spear]

but is x should be this right? = [ 1 0 0 , 0 1 0 , 0 0 1}?

for the first part

[deep condor]

well that's a matrix

[north spear]

yes

which we will split in 3

for e_1

e_2

e_3

[deep condor]

you mean $\vec{x} = c_1\vec{e_1} + c_2\vec{e_2} + c_3\vec{e_3}$?

[soft zealot]

haseeb

[north spear]

no

that a another type of question

[deep condor]

it is, but im trying to figure out what you mean by "x is the identity matrix"

[north spear]

look

this is from a another exam

we need to do like this

but here is a line instead of plane

so the formula is a bit diff

but its almost identical

x is always the identity matrix (mostly) in this question

but i was wondering if it the same if it have a reflection in the plane

[deep condor]

i have not seen a formula with a matrix to define a plane

usually it is two vectors

so i am unsure about this formula as you say it, sorry

[north spear]

nw fam

i think i am correct tho

double checked it with chat now

but i wanted to ask someone just if its 100% correct

.close

[final saddle]

Channel closed

Closed by @north spear

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[warm python]

If $P(E)=0.9, P(F)=0.8.$ Show $P(EF)≥0.7$

[soft zealot]

wai

[warm python]

So I have to write $E \cup F$ as the union of 2 dijoint events

[soft zealot]

wai

[warm python]

I'm losyt honestly

[versed crater]

Is P(EF) intersection

Like P(E ∩ F)

[warm python]

oops., yes

[versed crater]

Consider 2 cases

[warm python]

I guess $S \setminus(E^C \cup F^c)$?

[versed crater]

When E ∩ F = {} and when E ∩ F ≠ {}

[soft zealot]

wai

[warm python]

hmm?

[versed crater]

Wait am I being dumb

Okay I misread the question

.>

Use that P(E ∪ F) = P(E) + P(F) - P(E ∩ F)

[warm python]

Yeah, I used something similar I think

[versed crater]

Sorry I read a <= instead of >= in the question and confused myself

[warm python]

I would now like to prove Bonferroni's inequality

[versed crater]

The way I visualise this problem though is considering the unit interval

[warm python]

That is P(EF)≥P(E)+P(F)-1

[versed crater]

If I want 2 sets of lengths 0.8 and 0.9 then somehow the 0.9 and 0.8 sets needs to intersect at least 0.7 of the time

If you just for simplicity sake have the 2 sets as intervals then you’re kinda sliding these bars around looking at the overlap

[versed crater]

The left hand is bounded by 1 from above

It’s a probability so it’s bounded

[warm python]

This is confusing me

isn't this an equality

[versed crater]

Do you agree that this is true

[warm python]

yes

[versed crater]

Do you also agree that 1 >= P(E ∪ F)

[warm python]

sure

oh

[versed crater]

Then it’s straightforward

[warm python]

_<

got it

Have a few more questions I would like to solve here( All probability)

Show $P(EF^C)=P(E)-P(EF)$
\
$P(EF^C)=P(E)+P(F^C)-P(E \cup F^C)$
\

[soft zealot]

wai

[versed crater]

You just fiddle with the sets a bit

[warm python]

yeah

[versed crater]

I think it’s good to just wrestle with them for a bit

Like if you don’t get it immediately just keep trying

There aren’t all that much you can try so you’ll find it eventually

[warm python]

I think I'm almost there

Could I have a hint

.close

[final saddle]

Channel closed

Closed by @warm python

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rustic sinew]

Can someone validate my claim before i make a fool of myself being snarky?
Im helping zin with this problem and my claim is that the first and second derivative cannot be both strictly greater than and less than zero at the specified points

[ripe jewel]

it is sloppy writing

you are correct that at x=0, -2, 2 the criteria contradict

[rustic sinew]

It should be (-inf,0) and (0,inf)

[ripe jewel]

and (-2,2) etc

[rustic sinew]

Also parenthesis on infinity

Anyway thank you

.close

[final saddle]

Channel closed

Closed by @rustic sinew

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[nocturne depot]

$$\begin{problem}
Let $c$ be a nonzero real number. Suppose that
[
\left(c+\frac{1}{c}+1\right)\left(c+\frac{1}{c}\right) = 1.
]
Determine the value of
[
\left(3c^{100}+\frac{2}{c^{100}}+1\right)\left(c^{100}+\frac{2}{c^{100}}+3\right).
]
\end{problem}
$$

[soft zealot]

.
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[nocturne depot]

Mb lemme type it

Let be a nonzero real number. Suppose that

\left(c+\frac{1}{c}+1\right)\left(c+\frac{1}{c}\right) = 1.

\left(3c^{100}+\frac{2}{c^{100}}+1\right)\left(c^{100}+\frac{2}{c^{100}}+3\right).

If (c+1/c+1)(c+1/c)=1
Solve (3c^100+2/c^100+1)(c^100+2/c^100+3)

Ima close it and type it correctly

. Close

.close

[final saddle]

Channel closed

Closed by @nocturne depot

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[left wigeon]

how can we study the sign of tanx-x

[left wigeon]

using derivativs

the first derivative is sec²x-1

which AFAIK we cant reallybound it

.close

[final saddle]

Channel closed

Closed by @left wigeon

Use .reopen if this was a mistake.

[cinder whale]

any trig identities you can do with that?

[left wigeon]

i fugired out man

[cinder whale]

ok

[left wigeon]

btw i dont think you should reply in a closed channel

[cinder whale]

it sounded like you didnt resolve the question

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[left wigeon]

i closed it but i didnt specify mb then

[left wigeon]

.close

[final saddle]

Channel closed

Closed by @left wigeon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[gentle zephyr]

can someone explain the definition of quotient set?

[opal pelican]

A quotient set is a partition

Quite literally as simple as that

[gentle zephyr]

and if possible the fundamentaltheorem of equivalence relations

[gentle zephyr]

is more than that

[opal pelican]

Simply somewhat more formal

[opal pelican]

Trust me, at its core they're purely that

[gentle zephyr]

not every partition is a quotient set

[opal pelican]

Given an equivalence relation R, R induces a partition(quotient set) and any partition induces an equivalence relation

[opal pelican]

Actually, yeah

Pick some random set X and your favorite partition P of X

[gentle zephyr]

a partition of a set X is just the set of disjoint subsets of X

pairwise disjoint

[opal pelican]

Define an equivalence relation as follows: x~y iff x and y belong to the same set of the partition

~ is symmetric, reflexive and transitive

[gentle zephyr]

this is funda theo of equiv rela?

[opal pelican]

X/~ will again simply be P, the partition

[opal pelican]

Yup

[opal pelican]

The fundamental theorem of equivalence relations tells you this

[gentle zephyr]

a partition on a set is just a partition on a Set but a qoutient set of an equivalence relation is a partition on the set that the equivalence relation is defined on, such that every element in the partition is the distinct equivalence classes of the set that the equivalence relation is based of

is a mouthful, you understand?

[opal pelican]

I get what you're saying, I have worked with quotients multiple times

What I want to tell you is this: equivalence relations and partitions are in perfect correspondence

For any partition, there is a unique equivalence relation that induces it

And for any equivalence relation, there is a unique partition that defines it

Recall that any two given equivalence classes of an equivalence relation ~ are either equal or disjoint

From this follows what I told you above

[gentle zephyr]

yes, from which theorem you got this?

has this been proven, because i would appreciate it

[opal pelican]

Don't recall it having a name, it's just a lemma

[opal pelican]

I'll prove it to you right here

Consider a set X and an equivalence relation ~, choose two equivalence classes [x] and [y] from the quotient set, which we'll assume distinct

Assume then that their intersection is nonempty, choose some z such that z∈[x] and z∈[y], this then implies that z~y and z~x, however, by transitivity and symmetry we then have x~y, applying transitivity we obtain then that [x]=[y], as such, our assumption of a nonempty intersection must be false

To show that a quotient set is a partition you simply need to apply this and reflexivity to show that no element can be left outside of all the classes

[opal pelican]

Finally, for the second part of the theorem, that any partition induces an equivalence relation, simply apply this

Reflexivity, symmetry and transitivity are easily checked

[gentle zephyr]

how does it follow the union of the equivalence classes is the original set

[opal pelican]

Assume there exists some element z∈X such that z∉UX/~, then z is in no equivalence class, which implies z∉[z], in other words, ~ is not relfexive

[gentle zephyr]

you got a firm grasp on relations

why?

[opal pelican]

I've worked through my fair bit of set theory

Read Munkres' Topology chapter 1 on set theory on its entirety and am now wrestling with some more "formal" set theory

I found quotient sets to be a useful way to "isolate what's important"

[gentle zephyr]

how to prove the distinct number of equivalence classes is equal to the cardinality of the quotient set

[opal pelican]

By definition, no?

The quotient set will only include equivalence classes

As such, the number of distinct classes will be its number of elements

[gentle zephyr]

what's your definition of quotient set, does munkres define it?

[opal pelican]

The same as yours, a set of equivalence classes

And tbh I don't recall the exact definition Munkres gave

He was done with equivalence relations and quotients quite early

[gentle zephyr]

that's like a characteristic of it, but in set builder

[gentle zephyr]

damn

you said every equivalence relation induces a partition or every equivalence class onduces a partition?

[opal pelican]

X/~={x∈P(X):((z,y∈x)⟺(z~y))} would be the best I could come up with rn

[opal pelican]

Every equivalence relation induces a partition

With the quotient set being the partition in question

[opal pelican]

Yeah, he got quite far, by the end of Munkres I had proven equivalences of choice, worked with well-orderings, and much more

He also introduced zorn's lemma, ordering relations, the recursion theorem, and had some very interesting(but quite tough) exercises

[gentle zephyr]

this looks fine dude, interesting you could came up with it that quick

[opal pelican]

Well, thank you

[gentle zephyr]

what does topology has to do with this

[opal pelican]

Topology is all about sets

[gentle zephyr]

a friend of me asked me to define quotient set like half an hour ago and couldn't come up with the definition from the top of my head, i guess i need to prove more things with equivalence classes

[opal pelican]

So it requires some really strong background on (at least naive) set theory

[opal pelican]

Dw, you'll eventually get used to them, they show up quite frequently

And can be a handy tool at times

[gentle zephyr]

regarding an equivalence class of an element in X, how is it every element in the equivalence class is a candidate for class representative?

[opal pelican]

Because a class representative is no more than an arbitrarily chosen element of the class

So naturally, any element qualifies

Now, granted, you'll usually make use of something to choose the class representative

But any element could be one without a problem

[gentle zephyr]

is it possible that: a relation on A which is an equivalence relation is it possible that one of the equivalence classes of an element in A is empty? is it possible the quotient set is empty?

[opal pelican]

1:No, 2: only if X is empty

If an equivalence class is empty, there exists some element which is not equivalent to any element in the set

This includes itself, so the relation wouldn't be reflexive

[gentle zephyr]

🤔

[opal pelican]

2: the union of all the classes in the quotient set must conform the original set, if the quotient set is empty, then the union is empty and the original set is empty

[opal pelican]

What I mean by this is "if an element is not equivalent to any element it is not equivalent to any, including itself"

[gentle zephyr]

is defining an equivalence relation on an empty set imposible?

[opal pelican]

From this, it follows an empty class implies the relation is not an equivalence relation

[opal pelican]

Have you heard about vacuously true statements?

[gentle zephyr]

yes but i don't have a good example of one

is it more like you know it when you see it?

or am i just clueless?

[opal pelican]

A formula is false iff its negation is true

(assuming consistency but I won't get there)

So Imagine I said ∀(x∈∅)(|x|=ℵ_8727)

Is this true?

[gentle zephyr]

yes because there is none

no?

[opal pelican]

Indeed

Existential formulas are false for the empty set though

[gentle zephyr]

what is that aleph 8727?

[opal pelican]

But in general, any universal formula about Elements of the empty set will be true

[opal pelican]

The aleph indexed by 8727

[opal pelican]

Getting back to this, though, recall a relation ~ is an equivalence relation iff:
1:∀(x∈X)(x~x)
2:∀(x,y∈X)((x~y)⟺(y~x))
3:∀(x,y,z∈X)(((x~y)^(y~z))->(x~z)))

Notice all these are universal formulas

So if we take X=∅, essentially any relation between two elements you can define will be an equivalence relation over ∅

However, of course, these are not of much interest

[gentle zephyr]

ok

so it's vacuously true its reflexive symmetric and transitive because there is no element inside {}

[opal pelican]

Yup

[gentle zephyr]

so any relation defined on the emptyset is a equivalence relation

[opal pelican]

Yeah

So long as its definable

[gentle zephyr]

we are not saying anything useful, but is cool u clarify me this trivialities

because it May become handy somehow later

[opal pelican]

Well, all equivalence classes being nonempty Is a somewhat important fact

One of the reasons why reflexivity is needed

[gentle zephyr]

let's say i have an equivalence relation on the emptyset

for example, x ~ y <=> |x| <= |y|

this valid?

because the equivalence class of any representative is a subset of the emptyset, and therefore empty

[opal pelican]

Only problem I could find here is that you haven't defined addition for "elements of the emptyset"

That is, I don't see how you could turn this into a formula

[gentle zephyr]

now this?

i edited

[opal pelican]

Yeah, that works

That is an equivalence relation on any given set though

[gentle zephyr]

it's ~ defined on the emptyset

[opal pelican]

Yeah, that works

~ is an equivalence relation

[gentle zephyr]

then, there are 0 dustinct equivalence classes

[opal pelican]

With ∅/~=∅

[opal pelican]

Yeah, and exactly cardinality 0

[gentle zephyr]

yes

[gentle zephyr]

wdym?

[opal pelican]

The equivalence classes being nonempty implies the union of the quotient set is the original set

[gentle zephyr]

in this case every equivalence class is empty

[opal pelican]

And it stops quotient sets from behaving in a strange way

[opal pelican]

Yeah, but of sets with elements

[gentle zephyr]

ok

[opal pelican]

"is it possible that one of the equivalence classes of an element in A is empty*?

You implicitly assumed A was a nonempty set

Hence why I simply answered it wasn't possible

[gentle zephyr]

yes, right

im a dumbass srry

i don't even know what i am asking at this point

[opal pelican]

Nah, dw

[gentle zephyr]

but is cool we revised multiple examples

[opal pelican]

Well, I hope this helped you

[gentle zephyr]

yes thanks

.solved

[final saddle]

Channel closed

Closed by @gentle zephyr

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[cedar obsidian]

How did they write AB = sqrt440(1+x + x^-1), either on expanding this term doesn't give much idea from where did they get it

[subtle ginkgo]

they used the fact that the side of the second square sits along the hypotenuse in just such a way that by similar triangles:

(side of S₂) : (whole hypotenuse AB) = 1 : (1 + x + x⁻¹)

Since the area of the second square is S₂ = 440, its side–length is:

k = √440

[cedar obsidian]

not clear still

[subtle ginkgo]

what about it

[cedar obsidian]

side of S₂) : (whole hypotenuse AB) = 1 : (1 + x + x⁻¹)

[vital surge]

all are similar triangles, e.g. this diagram

[cedar obsidian]

yes

[cedar obsidian]

i didn't used similarity this this before ie ratio of the sides on one line segment

that is not clear

[vital surge]

"yes" so what is unclear

[cedar obsidian]

the side of the second square sits along the hypotenuse in just such a way that by similar triangles:

(side of S₂) : (whole hypotenuse AB) = 1 : (1 + x + x⁻¹)

this explanation

actually how are you applying similarity on hypotenuse

<@&286206848099549185>

[south crown]

I was waching gohar rn

Washp thoe

[south crown]

Are these the diagrams?

[vital surge]

if FE = s then
BF = as/b
AE = bs/a

because ACB is similar to GFB is similar to AED

tan(ABC) = x = b/a, so AB = AE + EF + FB = s(x + 1 + 1/x)

[final saddle]

@cedar obsidian Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lime crest]

Does a (non constant) polynomial always have a complex root? why and whats the proof?

[lime crest]

im just curious -w-

[tired walrus]

yes, and that statement is called the Fundamental Theorem of Algebra

which has many different proofs

https://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra#Proofs

[lime crest]

"atleast one complex root" so this doesnt mean that a degree n polynomial must have n many complex roots, right?

[tired walrus]

it does, by induction!

[lime crest]

oh cause factoring?

[tired walrus]

yes

once you prove that any nonconstant poly has at least one complex roots, this means you can start with a polynomial and pick off its factors one by one, bringing the degree down by 1 each time

[strange coral]

That’s only possible when the polynomial has complex coefficients

Otherwise not always necessary

[lime crest]

can you show some examples?

[strange coral]

Whatever

Like

x^2 + 2ix - 1 = 0

It has both roots i and i

[lime crest]

oh

i meant like the "not neccessary" part

[strange coral]

Oh

Let’s take quadratics

If all coefficients were real

Then if it had complex roots

It would always be two

And the roots would occur in conjugate pairs

if one root a+ib

Other would be a-ib

[lime crest]

the other a - bi yea i know this one

[strange coral]

Yes

[tired walrus]

@strange coral "complex" is taken in the inclusive sense here

we're not considering real numbers to "not be complex"

R ⊆ C and all

[strange coral]

well I interpreted it differently

[tired walrus]

and how did you interpret it

did you interpret "complex" to mean "not real"

[strange coral]

Mb

I was dealing with non complex coefficients

With imaginary part being zero

Otherwise, That would always imply that it would have complex root/ roots

[tired walrus]

i think you've introduced some confusion here

@lime crest do you have anything else to ask or anything else that's unclear

[lime crest]

nope, thanks you two! :3

.close

[final saddle]

Channel closed

Closed by @lime crest

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[warm python]

Given $P(A|B)≥P(C|B)$ , show $P(A^C |B)≤P(C^C|B)$

[soft zealot]

wai

[warm python]

I was thinking of starting like so'

$P(A|B)≥P(C|B) \iff A \cap B \supseteq C \cap B \iff A \supset C \iff A^C\subseteq C^C \iff A^C \cap B \subseteq C^C \cap B \iff P(A^C|B)≤P(C^C|B)$

[soft zealot]

wai

[desert mantle]

first equivalence is false

[warm python]

Well isn't P(A \cap B) ≥ P(C \cap B) true?

[desert mantle]

and?

[warm python]

isn't A \substeq B \iff P(A)≤P(B)?

[desert mantle]

no

[warm python]

It's only one way then

hmmm

[desert mantle]

you should be able to come up with a counterexample in <1 minute

[warm python]

A= R; C= \C; B=Q

[desert mantle]

what

[warm python]

$A =\R; B =\Q ;C=\C$

As a counter example

[soft zealot]

wai

[desert mantle]

with what probability measure

lets stay simple

finite

[warm python]

$A={1,2,3,4}; B={1,2,3}; C={1,2}$

[soft zealot]

wai

[desert mantle]

1. with what probability measure
2. not a counterexample

[warm python]

I'll have to think a bit

Honestly, I haven't done probability measure yet ( we haave in class, I haven't reached there yet)

[desert mantle]

ignore the word then

what distribution

I dont even wanna know what you think P is if not a probability measure

[warm python]

I'm lost

I'll revise this

.close

[final saddle]

Channel closed

Closed by @warm python

Use .reopen if this was a mistake.

[desert mantle]

.reopen

[final saddle]

✅

[desert mantle]

if you just say A={1,2,3,4}, then P(A) makes no sense

you need to say how the probability of A is calculated

aka you have to specify the distribution

or the measure

specify how P works

@warm python

.close

[final saddle]

Channel closed

Closed by @desert mantle

Use .reopen if this was a mistake.

[warm python]

Those are just the axioms of probability are they not

[desert mantle]

no

the axioms of probability say that P is a measure

they dont say what number P(A) actually is

[floral nova]

I think using the word measure, or even distribution is probably confusing them when you only really need to know that P is a function from some event space to [0, 1].

You don't need to know that the event space must be a sigma algebra, or what a measure is for this kind of Venn diagram chasing.

[desert mantle]

measure is a term you can introduce when you do the axioms of probability

terms like uniform distribution should be known already

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jade fable]

He,lo

[jade fable]

Hello

Eh

Hello

I’m a bit of tired and anxious but I want to maintain productive

I want a math game

That I can play rn

[tired walrus]

if you're tired and anxious then productivity is way lower on your list of priorities

[robust mulch]

that seems unproductive

[jade fable]

https://mathtrainer.ai this is the best I can find

Relaxing math game

But it lacks computation that involves fractions

As well as logarithms

[tired walrus]

do you want relaxation or do you want practice

you CANNOT have both

[jade fable]

I want something to grab my attention

[tired walrus]

ok then do something non-mathematical

watch a movie or play a non-math video game

[jade fable]

This activity has to be academic related

[tired walrus]

why?

[jade fable]

I want to use my time wisely

[tired walrus]

using your time wisely ≠ dedicating 100% of it to academics.

[jade fable]

You are right Ann

[tired walrus]

using your time wisely = knowing when to give your brain time to rest.

[jade fable]

I like reading novel

[tired walrus]

excellent, read some novels then

[jade fable]

Sure

The one I’m currently reading rn is the turn of the screw

[tired walrus]

remove one of "currently" and "rn"

[jade fable]

Yes,they are the same in meaning

[rustic crystal]

Try to fit as many calculations on a singular page as possible

It’s quite fun

or if you hate yourself, do that on a paper that already has stuff written on it

[tired walrus]

are you joking or serious

[rustic crystal]

It’s more fun than doing it normally, that’s for sure

[tired walrus]

you didn't answer my question

[rustic crystal]

Serious

[tired walrus]

then thats a terrible suggestion

[rustic crystal]

fair enough

You would be productive though if it works for you

It’s not as bad of an idea as turning all the stuff into individual paper cutouts that you can rearrange however you please until you solve it

that might actually be fun now that I think about it but you’d need a bunch of cutouts

(Also doesn’t work for everything)

[lime crest]

you basically want to be half-productive when you need to rest...?

seems silly to me

[final saddle]

@jade fable Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[upbeat shuttle]

for this question the answer says base must be positive, why is this the case?

[upbeat shuttle]

and is this true for all logs?

base cant be negative

[dapper hull]

yes bases cannot be negative nor 1 nor 0

[upbeat shuttle]

oh okay

is there any reason for this or proof i can see

just to understand

even if not ill just follow that lol

[tired walrus]

log_a(b) is the solution to a^x = b, which is supposed to exist and be unique

[dapper hull]

just think of 1^x=2 is this possible in the reals , same idea for 0 and the negatives

[upbeat shuttle]

this is impossible yeah ok i get it

[upbeat shuttle]

icic

[tired walrus]

if a=1 or a=0 then a solution either doesn't exist or there are too many of them
and if a<0 then a^x is a huge can of worms to even talk about

[upbeat shuttle]

ic

interesting

tysm!

logs interesting

.close

[final saddle]

Channel closed

Closed by @upbeat shuttle

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fluid salmon]

can someone please help me with questions ii-v?

[fluid salmon]

ah man i got the particular solution wrong

wait

waiiit

no

its wrong

[drowsy epoch]

Can you show your work?

[fluid salmon]

one sec

i took $x-1=e^{t}=> \frac{dt}{dx}=\frac{1}{x-1}, y(x)=Y(t), y'(x)=Y'(t)\frac{1}{x-1}, y''(x)=\frac{(Y''(t)-Y'(t))}{(x-1)^{2}}$

[soft zealot]

MichaelRafto

[fluid salmon]

then i replaced

and found the homogenous solutions: $y=c_1e^{7t}+c_2e^{-2t}$

[soft zealot]

MichaelRafto

[fluid salmon]

now i need the particular solution

i tried using $y_p=A(x-1)^{-1}$ and then deriving that 2 times but it doesnt seem to work

[soft zealot]

MichaelRafto

[fluid salmon]

$y'_p=-A(x-1)^{-2}, y''_p=2A(x-1)^{-3}$

[soft zealot]

MichaelRafto

[fluid salmon]

$(x-1)^{2}2A(x-1)^{-3}-4(x-1)(-A)(x-1)^{-2}-14A(x-1)^{-1}=(x-1)^{-1}$

[soft zealot]

MichaelRafto

[fluid salmon]

$2A+4A-14A=1$

[soft zealot]

MichaelRafto

[fluid salmon]

$A=\frac{-1}{8}$

[soft zealot]

MichaelRafto

[fluid salmon]

$y_p=\frac{-1}{8(x-1)}$

[soft zealot]

MichaelRafto

[fluid salmon]

...which isnt the particular solution

<@&286206848099549185> can't i just solve for x and not for t on this one?

[drowsy epoch]

I don't think you can guess that easily a particular solution, have you tried variation of parameters?

[fluid salmon]

what i wrote is what i did basically

(almost)

i will try with $y_p=Ae^{-t}$ now

[soft zealot]

MichaelRafto

[fluid salmon]

$y'_p=-Ae^{-t}, y''_p=Ae^{-t}$

[soft zealot]

MichaelRafto

[fluid salmon]

$Ae^{-t}-5(-Ae^{-t})-14Ae^{-t}=e^{-t}$

[soft zealot]

MichaelRafto

[fluid salmon]

$A+5A-14A=1$

[soft zealot]

MichaelRafto

[fluid salmon]

yup same thing

$A=\frac{-1}{8}$

[soft zealot]

MichaelRafto

[fluid salmon]

$y_p=\frac{-e^{-t}}{8}$

[soft zealot]

MichaelRafto

[fluid salmon]

$y_p(t)=\frac{-1}{8e^{t}}$

[soft zealot]

MichaelRafto

[fluid salmon]

isn't that the same thing? <@&286206848099549185>

[drowsy epoch]

For some reason both are correct actually

I suppose though, you solution is not an actual particular solution but a possible linear combination of your homogeneous solution

Hmm though I doubt that actually

[fluid salmon]

so $\frac{1-9x}{72(x-1)^{2}}$ is wrong?

[soft zealot]

MichaelRafto

[drowsy epoch]

No that also works, I checked on Desmos

[fluid salmon]

huh

[drowsy epoch]

https://www.desmos.com/calculator/ae4q9y458k

[fluid salmon]

how do i get this one then?

ig it doesnt really matter since both are correct

[drowsy epoch]

,w simplify (1-9x)/(72(x-1)^2)-(-1)/(8(x-1))

[soft zealot]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by adoniszgks

[drowsy epoch]

Yes they should be equivalent actually

In the homogeneous solution we have c_2/(x-1)²

So you could redefine the constant c_2 in such way so that you end up with the particular solution they have

[fluid salmon]

idk what that is

[drowsy epoch]

You just choose a new constant

So you get their particular solution

[fluid salmon]

aight

[drowsy epoch]

I suspect they just chose a different approach or did variation of parameters instead of guessing

[fluid salmon]

The proffesor's way is basically "take yp as Ae^nx" and find the particular solution for the equation"

[final saddle]

@fluid salmon Has your question been resolved?

[fluid salmon]

i'll come back to the exercises later i gtg

.close

[final saddle]

Channel closed

Closed by @fluid salmon

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[modest kettle]

TOPIC: Absolute Value & Piecewise Functions. Missed math class friday, dont understand very much from the notes and needed further explanation. Thanks!

[modest kettle]

need help with this problem specifically, dont understand what im supposed to do but i tried to start it

heres an example problem i copied the answer for from the notes if it helps

[swift void]

Okay so what do you get about absolute values, lets start with those since they are fairly simple

[modest kettle]

absolute value is the distance of a # from zero

[swift void]

Thats one way to say it, that the modulus. But as a function it makes everything inside positive

so |-5| = 5

[modest kettle]

okay, yeah that makes sense

[swift void]

Which is basically to say, -5 is 5 away from 0

But for intuition it is simply, everything is positive

So with the first function, everything from 5 and beyond is positive and the absolute bars do nothing. and form 5 and below everything is negative and thus the bars flip every output inside

Now to find specific points or ranges remember this simple rule: If the inside is negative, to remove the bars multiply the parts inside by -1. So the first function is 2((-1)(x-5))-4=2(5-x)-4 from 5 and below. and 2(x-5)-4 for 5 and above

[modest kettle]

idk if im understanding what your saying, but i tried solving the equation you gave me, what do i do with this information

[swift void]

almost, the negative one is distributed to all elements inside the ||

[modest kettle]

alr let me try afain

[swift void]

Now that i look back, it was written correctly

my bad 😂

$\mqty( 2x-6 & x>5 \ -2x+1 & x<5)$

[modest kettle]

where did the 14 come from?

[swift void]

Wow my bad

[soft zealot]

jelly v20

[modest kettle]

its all good my friend

[final saddle]

@modest kettle Has your question been resolved?

[final saddle]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[daring kraken]

how to find the intersection of y=3x+2 & y=4x-1

[severe canyon]

Ever heard of simultaneous equations?

Or system of 2 equations?

[daring kraken]

explainn 🤔

english isnt myfirst language so i probably know what u mean its just something different in my language , lol

[opal plinth]

samtidige ligninger

[daring kraken]

how did u know my first languagehello

[atomic moon]

Your status

[daring kraken]

but yes i believe i know such then 🤔 was watching a video of like
theyre both y= meaning u can put them together like 3x+2=4x-1 then find the x

[daring kraken]

OH right..

i got the whole gang here

[opal plinth]

So many people forget what information they display online

[daring kraken]

its a good song 😢

[atomic moon]

Seems good no ?

[daring kraken]

no because the issue is , i have no idea on HOW to find the x 🤔

like i never kknow when to add, remove, etc , on either sides

its quite confusing truly

[atomic moon]

Send all the x on one side

[daring kraken]

yes yes , i know such
but how 😆

[atomic moon]

And the others on the other side

[opal plinth]

Well then that's just manipulering af algebraiske ligninger

[daring kraken]

we really got the google translater here

[opal plinth]

I jest

[daring kraken]

but yes , i know what to do just not how haha

[opal plinth]

Try adding or subtracting the same quantities on both sides

Like you could add 2x on both sides and it doesn't change the equation

[daring kraken]

is it just trial and error then ? i have no way of knowing how to find my answer, onlu know that one side should be x and the other the answer

[opal plinth]

It's not trial and error no

[daring kraken]

woops

[opal plinth]

You have 3x+2 = 4x-1, what quantity can you add on the right side so that there's no more x there?

[daring kraken]

-4 ?

then id have -x on the left side no ?

[opal plinth]

Try

Show what you get afterward

[daring kraken]

but how do i remove the 2 or 1?!

[opal plinth]

Ok so you did the calculation correctly but the operation isn't to subtract 4, it's to subtract 4x

3x+2-4x = 4x-1-4x => -x+2 = -1

Yes?

[daring kraken]

oh yes! forgot to type that in haha , sorry

there we go

[opal plinth]

Right, well now you can add another quantity so that +2 disappears on the left

[daring kraken]

but then itd be -x+2-2=-1-2
would be
-x=-3?

[opal plinth]

Yes

You can also multiply by the same (non-zero) quantity on both sides

So as a last step here, you can multiply by -1

[daring kraken]

so -x*-1=-3*-1
would be
x=3?

[opal plinth]

Exactly

[daring kraken]

OH

😮

wow this is crazy

THANKS 🫡

[daring kraken]

so this would be the final answer yes?

its just some training assignemnts but i think i hav ethe hang of it now
Honestly just need to trust my gut more because i was going the right way before asking 😭

[opal plinth]

Well you probably want the y value as well

[daring kraken]

o

now

how we do that

so currently we have (3,y) right

[opal plinth]

Yes

Take either of the original equations, plug your value for x, solve for y

[daring kraken]

wat

[opal plinth]

Pick one of y=3x+2 or y=4x-1, replace x with 3, solve

[daring kraken]

right

[daring kraken]

11 🫡

3,y

[opal plinth]

(3, 11) is your answer

Or you can write x=3, y=11; depends what your teacher prefers I guess

[daring kraken]

yes! thank you

sent the assignment in at 10;45pm haha

its due september 2nd, was meant to send it early today but realized i forgot the last assignment so thank you for the help!

.close

[final saddle]

Channel closed

Closed by @daring kraken

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rich sonnet]

Hi there! I’m having trouble with an inverse function problem, specifically with how to deal with these variable exponents. Here’s the problem and the work I have so far

[drowsy epoch]

4x^y is not right

,, 4^y=x+4^yx

[rich sonnet]

Sorry for the quality, it says
a) find the inverse of the function f(x) = 4^x / 9+4^x

b) what is the domain of the inverse function?

[drowsy epoch]

Bring the y terms to the other side and factor 4^y

[rich sonnet]

I see!! Thank you

So 4y - 4^xy = x and then factor 4^y?

[drowsy epoch]

yes

also it's still 4^y not 4^x

[rich sonnet]

sorry I’m taking so long I’m trying to wrap my head around it haha

[drowsy epoch]

Do you know how to proceed, do you understand what happened?

[rich sonnet]

I think I see what you did, I read it as 4^(yx) rather than 4^yx

[drowsy epoch]

yes, don't

[rich sonnet]

Ok!! I understand, sorry about that. With this new equation, though, where exactly does the 4^y - 4^y * x come from? I understand 4^y(1-x) = x but I’m having a little bit of trouble understanding where you when from the factoring process

[drowsy epoch]

We moved the 4^y * x term from the right to the left side

[rich sonnet]

I see! That’s what I got as well ^^

[drowsy epoch]

Yes, now how would you proceed

[rich sonnet]

So from here, could we divide by (1-x) on both sides? In order to isolate 4^y

[drowsy epoch]

Yes

[rich sonnet]

Ok! Thank you

[drowsy epoch]

One last step

[rich sonnet]

Right, I’m a little unsure on how to deal with the variable in the exponent, would we be able to do anything with square roots?

[drowsy epoch]

No square roots or roots

We use logs

[rich sonnet]

Ok, got it! That makes sense I was wondering why we had this question in our logs assignment

[drowsy epoch]

There is a nice property, that is $\log_{a}(a^x) = x\log_{a}(a) = x$, \
provided that we have $a>0$ and $a\neq 1$.

[rich sonnet]

I see! And that’s law 3 right?

[drowsy epoch]

law 3?

[rich sonnet]

Sorry that might be something in my textbook only ^^’ we have 3 laws that we use for specific logarithms

Like this, I didn’t know if that was an actual name so that’s my bad

[drowsy epoch]

Yes, that would be law 3.

[drowsy epoch]

Specifically, we choose log with base 4 here because log_4(4)=1

[rich sonnet]

Aaa ok!! I was just about to ask if I could do that, awesome!

Thank you so much for your help I really appreciate it, is it okay to just leave it like that? Does it still count as a function?

[drowsy epoch]

You can simplify the left side

If you apply law 3, what will you get?

[rich sonnet]

ohhh I see, ylog_4(4)?

[drowsy epoch]

yes

Do you know the value of log_a(a)?

[rich sonnet]

I’m sorry I can’t think of anything😭 do they cancel out?

[drowsy epoch]

Yes

[drowsy epoch]

If the number inside the log and the base are the same, then the value is 1 😅

This is why we chose log base 4, specifically

[rich sonnet]

Oh!!!! Okok that makes sense!

[drowsy epoch]

Any log with different base would have worked, but it would make things more complicated

[rich sonnet]

Aaa alright alright I see, thank you!

Awesome!! Ok that makes sense, thank you!! I really appreciate the help ^^

[rich sonnet]

And I should be able to find the domain just by graphing, so I think I should be good… again tysm for the help, I hope you have a nice day!!

[drowsy epoch]

Oh if you are allowed, even better!

[drowsy epoch]

If you are done with your channel, you may close it with .solved

[rich sonnet]

Yeah! My professor is very lenient about it thankfully, I’ll definitely challenge myself in the future to do it without graphing lol

[drowsy epoch]

That's the spirit!

[rich sonnet]

Ty!! Is it better to use to close or solve command? I’ve been using close

[drowsy epoch]

Both work, I prefer solved

[rich sonnet]

Awesome, I appreciate it!

.solved

[final saddle]

Channel closed

Closed by @rich sonnet

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ivory island]

Can someone explain to me why this is the answer and not 2piy(9-y^2)

[ivory island]

oh

i get it

theres no limit on x axis

.solved

[final saddle]

Channel closed

Closed by @ivory island

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tranquil pine]

,,\int_{-1}^{1} \log [\frac{2-x}{2+x}], dx

[soft zealot]

!

[tranquil pine]

I have no clue on how to proceed

[burnt maple]

King's rule

[tranquil pine]

Oh

[desert mantle]

are those [] supposed to be floor?

[tranquil pine]

I think its called GIF

[desert mantle]

same thing

[valid carbon]

use \floor

,,\int_{-1}^{1} \log \floor{\frac{2-x}{2+x}} dx

[soft zealot]

Percy

[valid carbon]

f lol

$\big \floor$ ?

[soft zealot]

Percy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[tranquil pine]

Im getting the same ig

[valid carbon]

yeah nvm

at least its clear what it is

dont use square brackets

[tranquil pine]

Ok

[desert mantle]

$\lfloor \frac12 \rfloor$ I think? nope

[tranquil pine]

How to check if this is a odd or even function

Ye i don't know how to do, can somebody help

To solve step by step

[shell condor]

Alright, replace subtract x from the sum of limits

f(x) is your function

Now find f(a + b - x)

[tranquil pine]

We get the dame thing

Same*

[shell condor]

Are you sure?

[tranquil pine]

1-1 is 0 isnt it

[shell condor]

x is in minus too

1 + (-1) - x

[tranquil pine]

Then its the reciprocal

2+x/2-x