help-19

[faint knot]

thats about all I know about it

[next isle]

value function

[faint knot]

valuation function

[next isle]

i guess ill read some things on it

valuation

got t

it

is there anything that'd work with like the orders of arrays in math

[faint knot]

orders of arrays?

[next isle]

like

let r be the order

and let An = 6n-2

r = 3 is like

inputting n = 3

but the thing is

you dont have to have

6n-2

it can be like any set

where its

ordered from the smallest to largest

and r is the order in that set

[faint knot]

that does not at all explain what r is

[next isle]

i mean its really just series

[faint knot]

maybe another example should help

[next isle]

like A_r = 6r-2

its just a serie

but like

instead of

A_r = something

its just

it can be anything

for example

A = {1,3,6,29,394}

A_r_5 = 394

A_r_3 = 6

like an order function

like computer code but just mathematified

[faint knot]

thats called an index

[next isle]

oh yes

thats the bloody name

index

[faint knot]

yea

[next isle]

ive gone insane calling it r and order

[faint knot]

that is only loosely related to the collatz conjecture

[next isle]

its index 😭

[faint knot]

maybe you mistranslated ordinal

[next isle]

well

its sort of

not loosely related

i mean thats not how i ended up going w theres no other loop than 4-2-1

but it was the first idea i had

and it was pretty promising until i said the quote "Evens and odds fail to be enough as a proof to this"

and decided to try defining super-parity

which im still trying to see but its going harsh

saying 3 is more even than 5 is a tough challenge

[faint knot]

you can use the valuation function

[next isle]

yeah thats why i was interested

sounds like it

[faint knot]

I mean thats what p-adic numbers gauge their size by

Id do that

8 is more even than 4, and 4 is just as even as 12

[next isle]

i was really like mindblown by p-adics i feel like

[faint knot]

thats personally what I believe

[next isle]

that was going to solve it

until of course im stumped because im not very used to them

this really needs more expertise than a few weeks

[faint knot]

oh wait theres something off here, mb

[next isle]

but i geniunely see something i cant explain cuz i lack the math knowledge

[faint knot]

heres the valuation function but correct:

[next isle]

hm?

[faint knot]

you know what it acts like:
v(odds) = 0
v(2 * odds) = 1
v(4 * odds) = 2
v(8 * odds) = 3
etc.

sorry

log_2 of the numbers from before

[next isle]

yeah

[faint knot]

0 1 0 2 0 1 0 3 0 1 0 2 0 1 0 4

[next isle]

i noticed

that

[faint knot]

whoops

[next isle]

but i didnt question cuz idk what it is myself

felt odd

[faint knot]

me neither, I looked it up again because the mse post I linked raised 2 to the valuation

[next isle]

pretty much like, the first definition of super-evenness i had was

"how many multiples of 2 there is"

or

[faint knot]

you can see it like that

[next isle]

"2 has an even power"

but those definitions

also failed pretty badly

i think i have a new definition that works for different bases

[faint knot]

it shouldnt need to depend on base, unless youre referring to changing the 2 to a different prime number

[next isle]

i mean it looks interesting that

okay so actually

heres the thing that pushed me to think maybe i should use other bases and i can find patterns:

composite numbers in the -adics

veruss

versus

p-adics

so i was like

what if i use

a p-base

would i find something interesting

i mean its hard to understand what numbers im even writing so far

[faint knot]

you know all Im seeing so far is what was stated here

you save a lot of steps by grouping up a given multiple of 2 to divide as many multiples of 2 it has until youre done

[next isle]

i mean yeah thats

pretty

but like isnt that kind of

[faint knot]

we also have that T here for n > 1 is always odd

[next isle]

removing the 2s entirely

[faint knot]

its compressing the steps where you repeatedly / 2 if x is even

[next isle]

the 2s are actually very important in finding out there is no other loops

the reason why 1 loops is from what i've ruled only related to the fact that 1 is the only number not made up of primes

[faint knot]

or maybe 1 loops because (3 * 1 + 1) / 4 = 1

[next isle]

i mean this could help w the other part

[next isle]

a simple way to put what i found is like saying

every prime and every multiplication by 3 +1 will always lead to unique primes

its like

a trade off

your initial number loses some primes

and you gain some new primes

1 has nothing to lose

so it just loops

its the trading of primes that makes numbers uniquely follow

its like youre trying to stretch a rope infinitely, and try to connect both ends to make a circle

but the thing is you can only get so close to the other end

but it never loops because theyre all unique

[faint knot]

yea this is veering into crackpot territory for me

[next isle]

HAHAHA

[faint knot]

all Im seeing is that

if you consider only the powers of 2, they compress all the way to 1

and since 3 * 1 + 1 is a power of 2, its stuck there

[next isle]

thats a way to look at it

but i think thats the coincedence way

[faint knot]

for anything else, keep in mind that for an integer x, predicting the prime factorization of x + 1 is pretty difficult

[next isle]

thats the thing

[faint knot]

at least we know they are coprime, so every prime is exchanged

[next isle]

you dont have to predict it to say they're all unique

[faint knot]

but there isnt a pattern to be found here

[next isle]

because

lowkey, that was what i was trying at first

my goal was "how do you predict the outcome"

what if i predict the outcome will just be the way i want it to be, but i dont know the outcome?

[faint knot]

thats a standard math technique where you assume the form of an output then see if the rules allow for that form to be possible

[next isle]

the real thing is

heres teh thing

since theres infinitely many primes

its still extremely probable

that some number will trade off primes infinitely

and rise to infinity

i cant even like touch this problem

[faint knot]

that would go for any sequence outside of just collatz

I think what you should do is try coming up with an easier sequence based on collatz

[next isle]

$p \in \mathbb{Z}^+, m \in \mathbb{Q}^+; k,q \in {0,1,2}$
How do we prove that there exists or doesn't exist a certain ruleset for a function where $f: \mathbb{Z}^+ \rightarrow \mathbb{Z}^+$ is bijective for $f(x) =
\begin{cases}
p \mid x, & \frac{x}{p} +q \
p \nmid x, & mx+k
\end{cases}$

[clever fjord]

Red.

[next isle]

ts thing

[faint knot]

and are you, or are you not, asking about iterating f

[next isle]

yes

its not

bijective thingy

we discussd

[faint knot]

then you have to include that in the question

[next isle]

ill change the question

yeah

ill update it when

[faint knot]

you want to predict the cycles and divergence of f

[next isle]

i can

yes

reliably predict something

[faint knot]

moreover, having m be rational wont work

have m be an integer

[next isle]

yeah

i mean

the goal of me asking the question like this was

ive asked collatz

2 times

and got laughed at

so i decided ill hide collatz

in a more vague question

[faint knot]

we can see the collatz here

[next isle]

i mean yeah

its pretty obvious

[faint knot]

theres a reason people dont like collatz

[next isle]

i like it a lot

[faint knot]

its this

[next isle]

it gives me life and soul

[next isle]

oh yeah im afraid i might be re-doing a lot

[faint knot]

I think you should pick more approachable problems to find a life in cracking

[next isle]

but ive not been able to find anyone who told me

im not insane

for looking for a definition

[faint knot]

you need to start somewhere and collatz isnt going to be it

[next isle]

that says 5 is more even than 3

[faint knot]

5 is just as odd as 3 is

[next isle]

exactly thats what ive been told

which i respond

thats only because we only know basic parity

what if theres more properties to numbers than we think of

like when i think of properties

theres either some unique formula that outputs specific integers

or divisibility rules

[faint knot]

red you havent presented anything new or interesting here

[next isle]

or primeness

[next isle]

it would lead to something if i could get a hang of it

[faint knot]

this kind of question is why theres all sorts of freaky adjectives for numbers

[next isle]

freaky adjectives for numbers

[faint knot]

if you add another one, you need to have a reason for how useful this property can be

[next isle]

huhh

[faint knot]

red

[next isle]

reason why its useful:

it will be able to predict x+1's prime factors

i see something that i cant put to words because i lack the math knowledge to do so

or english

[faint knot]

so youre saying a version of parity that considers the parity of x + 1?

[next isle]

a version of some sort of a parity event that will predict x+1 depending on x

[faint knot]

maybe think of valuation here

no that wont work

heres the thing, predicting x + 1's prime factorization is already pretty hard

but you can reduce to just looking at one prime power

[next isle]

i feel like super-parity is lowkey just expanding parity from 2 | or not to n |

in a way

but it fails the same way

[faint knot]

doing n | for even n is just going to remove numbers considered with the same parity as 2

[next isle]

i think i've

almost gotten there

[faint knot]

I think you should stick to the valuation function

[next isle]

oh yeah ill look into that

tmr morning

[faint knot]

thats the conventional super-parity people use

[next isle]

perhaps it'll spark something

[faint knot]

oh one more thing

why do you have Log2(4) = 8 in your pfp

[next isle]

i am ahead by 2 years in my class in math, and they recently learned logs

then i asked my friend

smtn about them

and he said

[faint knot]

no way

[next isle]

"dude i didnt even listen to this shit"

and i said

"WDYM so if i said log2(4) what ru gonna say?"

he multiplied them and said 8

[faint knot]

lmao

thats amazing

[next isle]

and i like cranked a laugh in the midst of the metro

[faint knot]

keep it in

thats like the same way I got this laser pfp

someone posted a picture of god aiming a sniper at the pfp below them (at a diagonal) with a caption of "the next person who posts is gay"

standard issue image

but I came up with a solution

[next isle]

AHAHAHA

i see

[faint knot]

no one ever expects that when they ask for where my pfp comes from

I dont have a reason to change it so its always been like that

[next isle]

thats very unexpected yeah

[faint knot]

though now its more pixelated than before, because Ive lost the original image, so I had to screenshot my own pfp to replace it

[next isle]

i've had that happen

will i have to close this channel until further notice then

cuz like

its pretty stumped

[faint knot]

yea we aint getting far here

[next isle]

ill have to find some shit first

[faint knot]

you should try and look for an easier version of collatz to solve

[next isle]

i did

if i could id do it

i need more examples and hints and nudges

its like giving an Ai infinite computing power but no dataset

i need something to learn or work on that isnt just random mathematics around everywhere

i cant just learn all of math for a hobby in a few months

i wont give up tho

alr ill dip now

how do you close

.close

[odd edge]

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[nimble sail]

how do I prove this using induction

para todo = for every

[wooden cypress]

What have you tried?

[nimble sail]

Lemme show you a picture.

[wooden cypress]

Suer

[vital holly]

start by showing that
2n^2 >= (n+1)^2 for n>=4

[nimble sail]

I did.

[vital holly]

then the rest is just algebra

2^(n+1) = 2 * 2^n >= 2n^2 >= (n+1)^2

2 * 2^n >= 2n^2 is true by the induction hypothesis

[nimble sail]

@vital holly @wooden cypress

[wooden cypress]

How did you get from this line to this line?

[nimble sail]

That's just my induction.

[wooden cypress]

That is what you're trying to show, but you've just... asserted it

Unless I'm misunderstanding

[nimble sail]

Ah, no.

I don't know how induction works.

[wooden cypress]

Okay I'll give a quick rundown

For simplicity, let's call your statement P(n)

With induction, you would first show that P(4) holds

(or you could start with some other number, traditionally you start with zero but it really doesn't matter)

That's the base case

THEN you show that if P(n) holds, then P(n+1) must hold

So in this case that means you have to show that $n^2\le2^n\Longrightarrow(n+1)^2\le2^{n+1}$

[clever fjord]

depression

[wooden cypress]

You have to show this for any n >= 4

Then once you show those two things, that automatically means your statement is true for every n >= 4

That make sense?

[nimble sail]

It does

[wooden cypress]

Good good

You showed the base case already

So it's just the inductive step you have to worry about

[wooden cypress]

So have a crack at showing this

[odd edge]

@nimble sail Has your question been resolved?

[nimble sail]

Exactly, I don't know how to do that

[wooden cypress]

Okay

I suggest you rewrite (n+1)^2 in a way that lets you use the fact that n^2 <= 2^n

i.e. rewrite (n+1)^2 such that n^2 appears

[carmine idol]

(hint: you need to use the fact n>=4)

[nimble sail]

Okay, I can do that

n^2+2n+1

right?

@wooden cypress

[wooden cypress]

Good

So you want to show that $n^2+2n+1\le2^{n+1}$, and you know that $n^2\le2^n$

[clever fjord]

depression

[wooden cypress]

What do you think comes next?

[nimble sail]

I'm drawing a blank here

My intelligence is just that low.

[wooden cypress]

Well you can start from the left side

$n^2+2n+1$

[clever fjord]

depression

[nimble sail]

Yes.

[wooden cypress]

Then substitute in $n^2\le2^n$

[clever fjord]

depression

[wooden cypress]

What does that tell you?

[nimble sail]

That it should be smaller than 2^n + 2n + 1?

[wooden cypress]

Yep that's good

So now you want to show that $2^n+2n+1\le2^{n+1}$

[clever fjord]

depression

[wooden cypress]

Smaller than or equal to* but yes

[nimble sail]

What is next

[wooden cypress]

simplify it

[nimble sail]

How?

[wooden cypress]

Well there's a 2^n on both sides

You could subtract it

[nimble sail]

Well but one is 2^n and the other one is 2^n+1

[wooden cypress]

Yes but $2^{n+1}=2\cdot2^n$

[clever fjord]

depression

[wooden cypress]

$= 2^n + 2^n$

[clever fjord]

depression

[nimble sail]

Ah, true.

So we're left with 2n + 1 > 2^n

right?

[wooden cypress]

other way round

$2n+1 \le 2^n$

[clever fjord]

depression

[wooden cypress]

Also it's very definitely $\le$ not $<$

[clever fjord]

depression

[nimble sail]

Okay, what's next

[wooden cypress]

Loads of ways to show it

You could use induction

You also know already that $n^2\le2^n$ so you could show that $2n+1\le n^2$

[clever fjord]

depression

[nimble sail]

Let me see if I understand correctly.

[wooden cypress]

And that would suffice

[nimble sail]

How?

[wooden cypress]

Well $2n+1\le n^2\text{ and }n^2\le2^n\Longrightarrow2n+1\le2^n$

[clever fjord]

depression

[nimble sail]

Ah, I see.

Thank you man.

@wooden cypress should I quit this major?

It seems like only for smart people.

[wooden cypress]

This is your major?

What year are you in?

I'm not gonna tell you to do something like that, it really isn't my place

[carmine idol]

the basics of proving takes a while - then you need to recognise what proofs are doing so that you can check if your proof is sufficiently airtight

[wooden cypress]

But this should be (fairly) easy by quite early on in university so you should really work on it

I don't think you need to be that smart honestly but it's not easy

It just takes work

[carmine idol]

one way to view it is "play a skeptic who understands the class material"

skeptic: "prove n^2 less than or equal to 2^n"
you: "oh i just need to prove this base case and this inductive case"
skeptic: "why"
you: "that's how induction works"

you: "so since n^2 less or equal 2^n we have (n+1)^2 less or equal 2^(n+1)"
skeptic: "why"
[and you need to finish the argument here]

you can also understand the "skeptic" as "your classmates"

so when you get to higher-level classes, you don't necessarily have to show all the details, just enough for that sort of people

[wooden cypress]

I would still say you need to be able to show all the details but I get your point

[carmine idol]

there was once one of my profs gave a question that I thought was too easy and, I'm like ... huh... "my classmates" would probably skip all the steps and say that question is obvious, so I chose the skeptic to be the "lean proof assistant"

and idk, but i got the marks for that so i'm not complaining

some basic combinatorial lemma in representation theory

essentially index-wrangling

[wooden cypress]

@nimble sail I think the easiest way here is probably to just show $2n+1\le2^n$ directly by induction, rather than going via $n^2$

[clever fjord]

depression

[wooden cypress]

So what would the base case be?

[carmine idol]

eh, going via n^2 is quite easy too

especially given n>=4 restriction

[wooden cypress]

Yeah there isn't much in it I agree

[nimble sail]

Physics is my major

My second major

[carmine idol]

then well i guess you don't have to worry too much, but every math course would probably have some proving questions

whether induction is common would probably depend on the course too

[wooden cypress]

I wouldn't know - I've not done any physics since I was 19

But as an outsider, it does seem to be much more about calculation than proofs

Not to mention that there literally isn't any such thing as proof or truth in real physics

Having a firm grasp of how mathematical proofs work is never a bad thing though, especially since physics relies on a lot of mathematical results

[nimble sail]

What I'm saying is that maths seem hard, only for the clever.

And physics has a lot of maths.

[narrow crypt]

But physics has less rigor🥀

[nimble sail]

Well, still

I need to pass algebra 1

and algebra 1 is for physics

[wooden cypress]

Has your university given you a tutor? no idea how the system works wherever you're from

[nimble sail]

I didn't go to classes.

[wooden cypress]

If so you'd be much better talking to them about this than some random dudes on discord

[nimble sail]

So I don't really know.

Chemical engineering id easier, that's for sure

[wooden cypress]

Um okay

If you're not going to classes then what are you hoping to get out of university?

Changing major won't help with that

[nimble sail]

I wasn't able to go to classes, that's all.

[wooden cypress]

Are you at least catching up on the content?

[nimble sail]

I have a test in two weeks.

That's why I'm trying to learn this by myself.

[wooden cypress]

Fair

[nimble sail]

.close

[odd edge]

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[odd edge]

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• Show your work, and if possible, explain where you are stuck.
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[kind prism]

Yo so I went over this with someone else and we were kinda confused about the answer (π/2,2π) bc we though that it’s a cusp whenever both x and y equal 0 and that happens every 90°/0,pi/2/p… so I don’t get why it wouldn’t be like (0,π/2)(π/2,π)… and why it is what it is

[odd edge]

@kind prism Has your question been resolved?

[kind prism]

Hn

[rose radish]

what are u saying

[odd edge]

@kind prism Has your question been resolved?

[odd edge]

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Remember:
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• 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.

[pulsar kelp]

Can I get help with this math question? I understand the steps leading up to the one you have to fill in but I'm confused as to how you figure out which triangle congruence theorem to use. Given: △STU an equilateral triangle, ∠TXU ≅ ∠TVS

[pulsar kelp]

The question wants you to figure out what part of the proof has you using AAS as a reason

but idk what that is since its hard to visualize the statements

[brittle plinth]

consider the triangles that have the equal sides/angles leading to congruence by AAS

[pulsar kelp]

this geometry course is completely online so I'm not sure as to when each theorem is used

or what info you need for each one

[brittle plinth]

lemme color in the equal sides/angles to help better visualize

[pulsar kelp]

earlier in paint i drew the congruency lines but got confused and couldn't find anything

[brittle plinth]

I marked the equal sides and angles in the same color

you have to find two triangles that share the green angle

can you see which triangles are congruent?

[pulsar kelp]

wait this line isnt in the original picture

[brittle plinth]

?

[pulsar kelp]

wait nvm thats the bottom

[brittle plinth]

it is in here

[pulsar kelp]

mb

[brittle plinth]

wait so your question is...

yknow the steps leading up to the congruence

but you are questioning how to figure those out?

[pulsar kelp]

well its that the questions about congruency like this before had marks and stuff to show what angles and lines were congruent but this one is just a whole bunch of shapes i dont really know what to do with

plus it's in proof form so working backwards is also new

[brittle plinth]

ah so like if you remove all the steps in the exercise and you're left to figure it out blindly

you don't know what to do?

[pulsar kelp]

yeah

because i dont really know how to solve this normally

[brittle plinth]

first you have to analyze the givens

what do you get from the givens

so first statement is ∆STU is equilateral

from that you have to derive the properties

so you have ST=TU=US and 3 angles are equal to 60°

then you have angle TXU = TVS

[pulsar kelp]

is that given?

[brittle plinth]

which statement you mean?

[pulsar kelp]

^

[brittle plinth]

that is already given as you said above

idk how to get the angle symbol

[pulsar kelp]

okok

[shrewd trellis]

@brittle plinth can i get help on my ticket when you are free?

[brittle plinth]

ticket?

[shrewd trellis]

43

[brittle plinth]

isnt Alex dealing with that already?

@pulsar kelp alright going back

[pulsar kelp]

k

[brittle plinth]

so to a person who has done a lot of geometry problems like me, the congruency/similarity of triangles is the one you have to practice regularly and get a feeling to

[pulsar kelp]

i have this so far as kind of a visual reminder

[brittle plinth]

this is one of the more basic ones so the only tip I can give is

get a feeling to a few specific forms of congruency

in this picture can you see that the figure looks symmetrical?

[pulsar kelp]

yes

[brittle plinth]

You can probably see that the figure is symmetrical along this blue line

if you see some sort of symmetry you should ask yourself questions like "are ∆TUX and ∆TSV congruent?

from that you just extract as much information as possible

[pulsar kelp]

If I were to be solving this as a regular problem with just the question "Prove: UX ≅ SV" and the given info like "Given: △STU an equilateral triangle, ∠TXU ≅ ∠TVS" and a picture of the triangle, how would I do that? As in how would I solve the problem under normal circumstances with the different theorems and postulates like SSS SAS AAS and ASA?

like if it was just this

[brittle plinth]

you might have to reverse-engineer

like "how am I going to prove this?"

for a basic congruence problem like this you might link those to two triangles

and question yourself if those two triangles are the same how would you do that

[pulsar kelp]

well with the other problems it was just two triangles intersecting but this problem is like a whole bunch of triangles i dont know what to do with

like i just wanna know the steps to solving one of these

like if you can lay them out in order that would be great

[brittle plinth]

there's no easy way to determine from the start

for some problems you have to construct extra segments

[pulsar kelp]

could you solve it and then show me how you did it?

[brittle plinth]

there are actually a few ways to solve this

but I think what matters more is your thinking process that leads to the solution

[pulsar kelp]

like AAS?

[brittle plinth]

you shouldn't confine yourself to whatever it is SSS SAS AAS ASA

remember that this problem still only involves very few elements

like I analyze the givens first and got this

then I see few sides and angles that are equal length here or there

so i try to link them to triangles and see if they're congruent

just notice the equivalent elements and and derive the congruent triangles

if you can't prove something directly without triangle congruency don't even try to

like I don't recommending asking "how do I prove these two triangles with SSS"

rather, you should ask yourself "what equal elements lead to these two triangles being congruent?"

@pulsar kelp any questions?

[brittle plinth]

asking like this is like confining yourself to a deadend

[odd edge]

@pulsar kelp Has your question been resolved?

[odd edge]

Channel closed

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[blissful depot]

I have to solve this equation

[modest nacelle]

What does the bracket mean?

[blissful depot]

[x] is floor, i dont know how you call it

like floor of 1.25 is 1

and of -3.4 is -4

[faint knot]

why are there [] and {}

[modest nacelle]

Floor is this $\lfloor x \rfloor$

[clever fjord]

Xwtek

[blissful depot]

and {x} is fractional part, like the 0.4 and

[blissful depot]

yes, in romania we note it like that

for some reason

[faint knot]

[x] and {x} are standard notation for floor(x) and frac(x) in some areas

[blissful depot]

yeah we took it from the french

[faint knot]

thanks french

[blissful depot]

lol

[faint knot]

now what would {-0.5} be

[desert jolt]

Curly brackets are fpf I presume

[blissful depot]

anyways, ive gotten x = 29/12 after giving values to floor of x

[tacit wasp]

When you have both floor and mantissa showing up together, it is usually helpful writing all the mantissas in terms of floor, using the definition {a} = a - [a]

[blissful depot]

ah true

alright let me try that

[tacit wasp]

And then suppose [x] = n for some integer n. This way, you can bound x (from the bounds of x, you'll see there will be 2 subcases for [2x])

[blissful depot]

So i can say that x = n + f, where f = {x}

and n is [x]

[tacit wasp]

Yes

But instead of writing f for {x}, I'd write x - [x]

Hence x - n

[desert jolt]

That’ll be complicated

Since you cant sub for [2x]

You can say that though

[blissful depot]

yeah i got to that point

[desert jolt]

Honestly this seems more of a trial error problem but let me try it again

[blissful depot]

Ive gotten down to this

[jolly halo]

is there any other instruction or context given?

[blissful depot]

No

It literally just says

"solve the equation"

im trying to link with x-1 < [x] <= x

[desert jolt]

@blissful depot constraint the eqn with {x}

Assume [x] = some k1 and [2x] = k2

[blissful depot]

Okay

Just give me a second, I should eat breakfast

[desert jolt]

Sure

I'll work on it as well in the meantime

[odd edge]

@blissful depot Has your question been resolved?

[blissful depot]

I'm back, I thought of something

if {x} <= 0.5, then [2x] <= 2x+1

and i was thinking to have 2 cases, one with {x} <= 0.5, and one with {x} >= 0.5

[desert jolt]

Uh this is true for all x though

Because 2x is always greater than [2x]

[blissful depot]

ah true

i just said it above

oops

[desert jolt]

This is the end result of my calculations after constraining {x}

[tacit wasp]

Just, for curiosity, do you have the solutions?

[brittle plinth]

I found the easiest method is to prove that {x} cant be >=0.5

[blissful depot]

i only found a few

by tries

ive found 29/12

and 19/6

there might be more

[brittle plinth]

from that you see [2x]=2[x]

using inequalities is enough to restrict [x] so you only need to try 4 or 5 values

[tacit wasp]

No, I mean, from the answer key of the book or teacher's notes
By the way, I've also found those 2 👍

But I also found a third one, 97/24

[brittle plinth]

I found that 97/24 works as well

[tacit wasp]

Awesome

[brittle plinth]

those are the only 3 according to my method

[tacit wasp]

If you want, I can send how I've solved it (with the spoiler of course)

[blissful depot]

There are no answers, its an old book

[brittle plinth]

what method did you use

[blissful depot]

I had to write the problem in latex because it had ancient writings

[tacit wasp]

I just splitted in two cases

[brittle plinth]

I kinda split into 2 cases

but I use inequalities to restrict [x]

btw is it true to say that [2x] = 2[x]+1 if {x}>=0.5?

[blissful depot]

Ok i got the idea, ill try to solve it myself

from the splitting part onwards

[tacit wasp]

I'm just sending the solution (hoping I didn't make any mistake)

Feel free not to read it until you've solved it

[weak crystal]

Can I ask my question here?

[blissful depot]

Yeah I wont

[brittle plinth]

open a new channel

[blissful depot]

open another channel for yourself

[tacit wasp]

!occupied

[odd edge]

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).

[tacit wasp]

Here it is @blissful depot

[blissful depot]

Alright, thanks

ill open it if im stuck

[brittle plinth]

ooh that's long

[blissful depot]

you're scaring me lol

[tacit wasp]

Yeah I wondered if I could shorten a little bit, but I didn't figure out how

[brittle plinth]

my solution:
||Split into 2 cases:
Case 1: 0.5<={x}
Then [2x] = 2[x] + 1
We have 4/3> 1/[x] + 1/(2[x] + 1) >= 5/6
[x] have to be positive since if [x] <= -1 the term will be negative as well
solving the inequality we get 1<[x]<=1.66 -> impossible

Case 2: {x} < 0.5
Then [2x] = 2[x]
Then we get 5/6> 1/[x] + 1/2[x] >= 1/3
Or 5/6 > 3/2[x] >= 1/3
Again [x] must be positive
Solving the inequality we get 1.8 < [x] <= 9/2
So [x] must be 2, 3 or 4
We can rearrange to get x = 1/[x] + 1/2[x] + [x] - 1/3
Plugging in [x] = 2,3 and 4 we get x = 29/12, 19/6 and 97/24, all 3 solutions are valid since {x} < 0.5||

[odd edge]

@blissful depot Has your question been resolved?

[blissful depot]

I have to prove that {x} <0.5 tho

oh wait i confused the cases

nvm

yeah i did the first one

Yeah i got it

I solved it

thanks for the hints, ill look over your solves too so I can see different approaches

have a good day!

.close

[odd edge]

Channel closed

Closed by @blissful depot

Use .reopen if this was a mistake.

[desert jolt]

Feels like you took a very long route here

[tacit wasp]

I'm not an expert about this 🤷‍♂️

I've just done what I was able to do and what came to my mind at first

But sure, I agree it's a bit long

Or, rather than long, there are many calculations

[odd edge]

Available help channel!

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[fast slate]

can someone help me in a simple problem

[narrow crypt]

Send the question

[fast slate]

correction for the number, there's 7 teachers we're supposed to make them like ordered pairs

can someone tell me if my answer is correct?

i got

(1,1) for mrs andres for perdev
(1,1) for sir lorilla for genchem
(1,1) for ms alba for kompan
(1,1) sir abella for oral comm
(1,2) for sir turcido for pre-cal and gen math
(1,1) for ms manzano for pe
(1,2) for ms gonzales and earth sscience

is it wrong?

lmk if yall kno

i hope yall gaf

[wooden python]

where's the actual question?

[fast slate]

oh uh theres no actual question

[wooden python]

then there's nothing to do

[fast slate]

my teacher just showed me that

were supposed to make them like um ordered pairs?

[wooden python]

so you do not have the actual, full instructions written down anywhere.

is that what you're saying?

you're only going by half-remembered things that were only spoken in class but not written down?

[fast slate]

er no my teacher did not give the full instructions

[wooden python]

ok then again there's nothing to do

[fast slate]

all he said was make the subject andnthe object in ordered pairs

[late sinew]

What is a subject and object

Define them

[fast slate]

what i meant was subject = literally subject and object = the teachers

im asking if my answers r correct

[late sinew]

Ok its correct then

Except that you married off ms andres

[fast slate]

can the domain be repeated

[late sinew]

What domain

These arent functions

[fast slate]

what

ordered pairs

[late sinew]

You're not making sense

[fast slate]

no offense but no shit were still learning this lesson

dont expect me to knwo everything

i wouldnt know if ur not explaining it to me properly

[late sinew]

I'm expecting you to know what you mean by domain

Do you mean 'a' in the ordered pair (a,b)?

[fast slate]

yes

[late sinew]

Well which is why i said this

What you've done is correct, you can repeat a in different ordered pairs (a,b)

[fast slate]

huh thats weird my classmates said its functions

[late sinew]

These are not functions

[fast slate]

then relations...?

[jolly halo]

i mean domain can be used in context of relations

but im really not able to understand what type of pairs you have created tbh

do you have a example question , or a reference question

some question which had similar objective

[fast slate]

lol no my teacher js dropped thisi right infront of my face

and told us to make these in ordered pairs

.close

[odd edge]

Channel closed

Closed by @fast slate

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.

[pallid trellis]

I'm supposed to find angle bd but idk what formula I'm supposed to use.

[pallid trellis]

I was thinking cosine

But I just want to make sure

I just learned how to do these like yesterday night so I'm not really a professional at hyputunus thearom

[vivid wyvern]

Yes u can use that

[pallid trellis]

Ok

[vivid wyvern]

But do u know which angle u need to consider for it?

[pallid trellis]

40?

[vivid wyvern]

Yes

[pallid trellis]

Ok

[vivid wyvern]

U got this then,give it a shot

[pallid trellis]

What am I supposed to write on my calculator then?

Cos40 9/14?

[vivid wyvern]

Do u what the cosine of an angle means?

[vivid wyvern]

Nope

[pallid trellis]

Ah

[vivid wyvern]

I'll walk u through it

[pallid trellis]

ok

[vivid wyvern]

So cosine of an angle means the ration between the base of the triangle on the basis of the angle and the hypotenuse of the triangle

When u consider an angle of a right angled triangle other than the right angle
U need to identify which one is the opposite side and which one is the adjacent side

[pallid trellis]

yea i wrote em down im pretty sure

[vivid wyvern]

Adjacent side is also called base
And Opposite side is also known as perpendicular

[pallid trellis]

perpendicular height?

[vivid wyvern]

Okay so can u identity the adhacent and opposite sides?

[pallid trellis]

yea

[vivid wyvern]

Yeah same as opposite

[pallid trellis]

wrote em down look

[vivid wyvern]

So which one is the adjacent side of 40°

[pallid trellis]

hypotenus

oh wait

opposite

[vivid wyvern]

Oops i hv been wrong all along

Ok then no we cant use cosine

[pallid trellis]

oh man

[vivid wyvern]

Sorry

[pallid trellis]

??

how

[vivid wyvern]

Instead we need to use tan

[pallid trellis]

oh

[vivid wyvern]

Cosine involves adjacent and hypotenuse

[pallid trellis]

yea

[vivid wyvern]

But we need to find the opposite

[pallid trellis]

i need to find line bd

in cm

[vivid wyvern]

So u need a trigonometric function which involves opposite

[pallid trellis]

which is opposite yea

[vivid wyvern]

Yes

So which functions involve opposite

[pallid trellis]

ong can we use sine too?

[vivid wyvern]

Yes

[pallid trellis]

we could sine too no?

yea

mr smart

[vivid wyvern]

Exactly so which one do u want to use

[pallid trellis]

sine

[vivid wyvern]

Yea man👍

[vivid wyvern]

Okay so what is the sine of 40°

[pallid trellis]

bet lets use sine

what does that mean

[vivid wyvern]

I mean sine of an angle refers to a ratio right?

[pallid trellis]

hmm

[vivid wyvern]

What is the ratio

[pallid trellis]

ah yes

40:14

[vivid wyvern]

Okay lemme explain

Sin of angle refers to the ratio of the opposite and hypotenuse

[pallid trellis]

ahh

so x:14

[vivid wyvern]

Do we agree?

[pallid trellis]

since we dont know opposite

[vivid wyvern]

Yeah x is BD here

[vivid wyvern]

Yea

[pallid trellis]

ahh okay

great

[vivid wyvern]

So sin of which angle is x:14?

[pallid trellis]

40

[vivid wyvern]

Now can u find the value of x?

[pallid trellis]

560

40x14=560

[vivid wyvern]

No that's not how it works

Lemme type it out

[pallid trellis]

oh

[vivid wyvern]

sin(angle)=opposite/hypotenuse

[pallid trellis]

oh yea

its written on mah paper

cool

[vivid wyvern]

So u need to put sin(angle)
Not js the angle

[vivid wyvern]

Try it out

[pallid trellis]

so sin14=x/14

i meant sin40

shucks

sin40=x/14

and if we switch

x=sin40x14

oh dang

then we get x

and x is the opposite angle

ong im so smart

[vivid wyvern]

Can u give me the length u got

[vivid wyvern]

X is called the "opposite side" ,not the angle

[vivid wyvern]

And yes u r👍

[pallid trellis]

9

9cm

?

[vivid wyvern]

Yeah

[pallid trellis]

bettt

[vivid wyvern]

When we approx it out

Ok good job

[pallid trellis]

ok now i need to calculate length of dc

[vivid wyvern]

Ok so u hv BD now ryt?

[pallid trellis]

yes

i need to find dc now

[vivid wyvern]

So in triangle BCD

[pallid trellis]

we use tengant right?

bet we use tangant

[vivid wyvern]

Yea

Go on and let me know ur answer

[pallid trellis]

whats the formula of it again?

tangant=opp/adj?

ong it has to be

[vivid wyvern]

Hm

[pallid trellis]

im supposed to use angle 55?

[vivid wyvern]

Yes

[pallid trellis]

ok

[vivid wyvern]

Uk why ryt?

Actually u can use both

55 and 35

[pallid trellis]

actually

i dont know why

i just guessed

[vivid wyvern]

Okay so lemme explain

Tangent of an angle is the ratio of opposite and adjacent as h said

[pallid trellis]

ye

[vivid wyvern]

So when we choose an angle we need to check if the adjacent and opposite of that angle involves the values of the length we need and the length we have

[pallid trellis]

mhm

[vivid wyvern]

Js a note if u didnt know the way to identify which one is opposite and which one is adjacent is the side opposite to the angle is opposite and the other is adjacent

[vivid wyvern]

If u dont understand let me know

[pallid trellis]

ahh

i get it now

alr

thanks

also dc is 10.7 corect?

ngl u made me become smarter

even though im already am

[vivid wyvern]

No wait

[pallid trellis]

?

its 10.7 no?

[vivid wyvern]

It's coming out wrong

[pallid trellis]

shucks

[vivid wyvern]

Can u tell me how u got that

[pallid trellis]

i did tang=opp/adj

yes?

then

[vivid wyvern]

Yeah

Tell me the values u used

[pallid trellis]

ah wait let me calculate again

i think i did 50 instead of 55

💀

[vivid wyvern]

Ok redo

[pallid trellis]

ah okay

12.9

[vivid wyvern]

Huh

How

Walk me through ur steps plz

So which angle did u use

[pallid trellis]

55

and 9

9 cm

[vivid wyvern]

What's ur opposite

[pallid trellis]

and 55

9cm is my opp

[vivid wyvern]

What's ur adjacent

[pallid trellis]

adj is 12.9cm

and the angle is 55

[vivid wyvern]

Nope it isnt

Okay listen

[pallid trellis]

how ong

this is doo doo

[vivid wyvern]

Tan(55)=opposite/adjacent

Ryt?

[pallid trellis]

yea

thats what i did

[vivid wyvern]

Tan(55)=9/adjacent

[pallid trellis]

yes

alr

[vivid wyvern]

Ik where u went wrong ig

[pallid trellis]

yea i get that

eh?

i then switched tan55 with adj

and it became x

what the heck??

[vivid wyvern]

Wait am i wrong

[pallid trellis]

then i got adj=tan55x9

[vivid wyvern]

No i m fine

[pallid trellis]

ong im right

[vivid wyvern]

No

[pallid trellis]

nvm

[vivid wyvern]

That's where u wrnt wrong

[pallid trellis]

ok

[vivid wyvern]

U see to find adjacent u need to take the adjacent to the other side

And bring tan(55) below 9

[pallid trellis]

yea..

[vivid wyvern]

That makes it 9/tan(55)

Ryt?

[pallid trellis]

no

[vivid wyvern]

Why

[pallid trellis]

because if tan55 hops over the equals sign it becomes times

because the opposite of division is times

👍

[vivid wyvern]

Yea but tan55 isnt in divided form

It is in times form

With 1

[pallid trellis]

but the adj is

[vivid wyvern]

Yeah so the adj is multiplied

With 1

And tan55 is divided

[pallid trellis]

ahh let me check

hmm yk what

it makes sence

cuz the line next to it

is 12 cm

and it CLEARLY shows that that line is smaller then the 12cm one

so in the end

[vivid wyvern]

Ah lemme show u

[pallid trellis]

its 6.3cm

[vivid wyvern]

Exactly

[pallid trellis]

boom ez

im too smart

[vivid wyvern]

Yeah good

[vivid wyvern]

Alr js think abt what u do with a calm mind
And u will do great

[pallid trellis]

bet

hmm

this is hard one now

im supposed to find angle 0

what am i supposed to use?

i only know how to find sides wth

[vivid wyvern]

Ok it's still trig

Look at which sides r involved

On basis of theta

[pallid trellis]

so tangant?

[vivid wyvern]

Nope

[pallid trellis]

oh man

[vivid wyvern]

See u hv two sides given

Try to understand

[pallid trellis]

ahh

its sign

sine

well if u do sign

sine

u find opposite

i need anglie what

oh wait

[vivid wyvern]

Wait

[pallid trellis]

its cosine

innit?

[vivid wyvern]

Yea

[pallid trellis]

bet

ong what

whats this

i did cos=12/14

im supposed to write that right

?

oh wait

its none of the above

because you dont have an angle ready for ya

[vivid wyvern]

Ok

[vivid wyvern]

Wait

Did u learn inverse

Like cos^-1

[pallid trellis]

oh yeaa

-1 means over right?

[vivid wyvern]

Like in calculator u can press thst

[pallid trellis]

1 over

[vivid wyvern]

Yes

[pallid trellis]

ok what am i supposed to write?

[vivid wyvern]

So cos(theta)=12/14

Theta=cos^-1(12/14)

Lemme know if u dont get it

[pallid trellis]

wats theta

i dont have that in my calculator

meh i just wrote it without theta

[vivid wyvern]

Theta is the angke

[pallid trellis]

i got 31 degres

[vivid wyvern]

Yeah u dont need to put theta in ur calculator

[pallid trellis]

ok

its 31?

[vivid wyvern]

Yeah

U r ryt

[pallid trellis]

ok

[vivid wyvern]

Yep

That's how it works

[pallid trellis]

so when do you use sin-1?

or cos-1

or tan-1

in angles only right?

[vivid wyvern]

When u need to find angles

U use those but it depends on which sides u choose basing on the angle

For sin ,it's opposite/hypo

For cos it's adj/hypo

For tan ,oppo/adj

[pallid trellis]

ok

alright im done

thx

u made me more smarter

bye

[vivid wyvern]

Good work

[pallid trellis]

how to close

/close this damngod ticket

/ticket sleep

[glossy smelt]

What’s the best website to start studying for math 3

I live in nc

[pallid trellis]

chatgpt

[glossy smelt]

Actually?

[pallid trellis]

yes bro

[glossy smelt]

What do I enter as the prompt

[pallid trellis]

just give the question and u got the answer