Why is that?
#help-27
deep quartz
~~y/x - x/x = x
let (y - x) = z
(y - x)/x = z/x
w/x - y/x = w-y/x
2/3 - 1/3 = 1/3
5/7 - 3/7 = 2/7
w/x - y/x = w-y/x is what should have been written.~~
vast rain
Why is that?
why do I think you're not going to get anywhere? because I'm pretty sure the things that you're using have already been proven to be consistent within ZFC (i.e. what you're trying to do is IMPOSSIBLE if you take the axioms of ZFC)
deep quartz
why do I think you're not going to get anywhere? because I'm pretty sure the thi...
What is ZFC?
89/221 - 23/221 = 66/221
211/5683 - 677/5683 = -466/5683
w/x - y/x = z
w/x - y/x = w-y/x
???
seems like the problem could be intrinsic to the function of the order of operations maybe
big maybe
it's like there's /something/ missing there, besides the parenthasis (lol), but I can't place ot
it
vast rain
seems like the problem could be intrinsic to the function of the order of operat...
that's one way of looking at it, but the other way of looking at it is that what you've written is not true
like sure you could define your own order of operations to make it true
deep quartz
I know what I'm writing must technically be
w/x - y/x = (w-y)/x
but how/where?
vast rain
but the order of operations is a convention for written mathematics so we don't have to stick parentheses everywhere
deep quartz
like sure you could define your own order of operations to make it true
I would enjoy that tbh. But idk it I could ever accomplish something so grand as that.
vast rain
there's nothing grand about it
deep quartz
but the order of operations is a convention for written mathematics so we don't ...
Interesting. Can you show me how it might look if were were to do some math with all those parenthesis instead of conventional order of operations?
deep quartz
there's nothing grand about it
Beauty and the eye which beholds it.
vast rain
no it's like the difference between writing in cursive and in print
deep quartz
the parentheses are considered implied
When and where?
vast rain
or changing fonts on your computer
like 4 + 5/4 + 2*4 is written with all parentheses as 4 + (5/4) + (2*4)
deep quartz
like 4 + 5/4 + 2*4 is written with all parentheses as 4 + (5/4) + (2\*4)
Do you know why that is? I have a few publications about it saved somewhere but I haven't read them yet.
vast rain
and both mean the same thing: "4 plus the quantity 5/4 plus the quantity 2*4"
vast rain
Do you know why that is? I have a few publications about it saved somewhere but ...
it's just defined that way
it's like asking why the English word for mathematics is spelled that way
deep quartz
Like why is order of operations as it is? I know it involves addition as the "base" binary operation
vast rain
it's defined that way so we can easily communicate the underlying mathematics over text
in fact, there are other forms of notation like postfix and prefix notation that do not require an order of operations
deep quartz
That is interesting. I'll have to look into that.
vast rain
because they do not require parentheses
but these are just notation
they have nothing to do with the underlying mathematics
it's literally like writing something in another language or changing the font on your computer
or writing in cursive instead of print
the underlying ideas and concepts are exactly the same
the underlying mathematics is exactly the same
deep quartz
the underlying ideas and concepts are exactly the same
But what are those concepts? Which dictate the...well, order of the order of operations?
vast rain
no
the concepts do NOT dictate the order of operations
the order of operations is ARBITRARY
it's something picked so we can communicate effectively
like picking a common language with someone else so they understand what you're talking about
or picking definitions of words or symbols so we're talking about the same thing
the underlying concepts are the same, no matter if you speak it in English or Portuguese
likewise the underlying mathematics is the same, no matter what notation you use
deep quartz
the underlying concepts are the same, no matter if you speak it in English or Po...
So then we simply must multiply and divide before we add and subtract, but must do so sequentially, for both sets of operations, just because? Because we simply must?
vast rain
So then we simply must multiply and divide before we add and subtract, but must ...
no it's not because you "must"
mathematics is not because of "must"
deep quartz
I suppose maybe I am not quite understanding you on this, but I want to.
vast rain
it's that people have decided that this is what THE WRITING means
when someone writes those squiggles on a paper
we have a common understanding what those squiggles mean
what they express
that is what the order of operations is part of
deep quartz
it's that people have decided that this is what THE WRITING means
I am a conlanger and linguist moreso than a mathematician, but you've really lost me. I'm sorry. I am trying to understand.
deep quartz
So the order of operations is part of a common understanding. That kinda makes sense. What is that understanding then?
vast rain
it is the understanding of how to interpret what the writing means mathematically
do you read sheet music?
deep quartz
do you read sheet music?
Years ago, and only for the trumpet.
But yes. Just modestly so.
midnight dirge
sheet musics a hoax
vast rain
I'm sure you're aware that people can basically call the dots on the paper whatever notes they want
but it is the clef that determines what the notes actually are
midnight dirge
sry i shld stop saying that, ill be taken seriously
deep quartz
sheet musics a hoax
SHEET MUSIC: EXPOSED
restive river
its just chosen that way to make writing most formulas more easily, it requires less brackets that way most of the time. We couldve also chosen to do addition first and then multiplication:
1 + 2 * 3 = (1 + 2) * 3
but we didnt
midnight dirge
yea nvm ignore me
deep quartz
sry i shld stop saying that, ill be taken seriously
no don't stop I like you lmao
vast rain
we have adopted a CONVENTION that when people write some squiggly thing 🎼 next to the sheet music
that the note on the bottom line is an E
nothing in music says that the note on the bottom has to be middle E
deep quartz
So order of operations is how it is because "when we write this next to this we do this with this and that to this and/or that because that" is basically what you're saying except less convoluted
vast rain
order of operations is part of the set of conventions that we use to interpret the symbols written on paper
some other conventions include:
"+" means addition
"*" means multiplication
"-" means subtraction
consider the expression 5 + 3/4
with the order of operations, this means, unambiguously, divide 3 by 4, and then add that quantity to 5
deep quartz
but it is the clef that determines what the notes actually are
I just saw this and it kinda struck a note with me (pun intended)
vast rain
it is a shorter, more convenient way of writing 5 + (3/4)
but these two things are mathematically IDENTICAL
they're the same CONCEPT
just written in different ways
deep quartz
with the order of operations, this means, unambiguously, divide 3 by 4, and then...
Why not just write 3/4 + 5 and then do all math sequentially ffs? ?___?
vast rain
Why not just write 3/4 + 5 and then do all math sequentially ffs? ?___?
that is what prefix and postfix notation do
unfortunately people's eyes aren't great at it
your system doesn't work for many reasons
but smart people have invented notation systems that do NOT require parentheses or an order of operations
deep quartz
your system doesn't work for many reasons
May I will find comfort with this prefix/postfix notation system.
midnight dirge
but smart people have invented notation systems that do NOT require parentheses ...
yea, sometimes looks disgusting without lmao
deep quartz
but smart people have invented notation systems that do NOT require parentheses ...
That might be what I've been seeking. Something more...real? true? idqke
midnight dirge
thats new
deep quartz
"negate increase sustain divide indetermintes a, b, and c"
is my best incorrect guess xD
vast rain
That might be what I've been seeking. Something more...real? true? idqke
how can you say that it's more real or true
deep quartz
I was just kidding
vast rain
that's literally saying that English is more real than Portuguese
deep quartz
how can you say that it's more real or true
I should rather have said that it just sits better with me for some reason.
vast rain
they're just different ways of writing the same thing
vast rain
I should rather have said that it just sits better with me for some reason.
that's like saying that cursive sits better with you than printed handwriting
deep quartz
Resonates with me in a more agreeable way that conventional notation. Perhaps.
deep quartz
that's like saying that cursive sits better with you than printed handwriting
Is that not a valid stance to maintain if it were the truth?
deep quartz
but that makes absolutely no sense
Then how did I just understand it? And how did you write it to begin with?
vast rain
Is that not a valid stance to maintain if it were the truth?
no? both communicate the same thing
neither is less valid than the other
deep quartz
neither is less valid than the other
I can appreciate that valid stance that you have just maintained.
vast rain
just because you don't understand why an order of operations is important doesn't mean that the standard math notation is somehow worse than nonstandard ones
for one, infix notation is much easier for humans to compute because it's intuitive
deep quartz
cat cactus tree pollo guut daas dane
except phonetic
deep quartz
for one, infix notation is much easier for humans to compute because it's intuit...
That is true to me.
deep quartz
just because you don't understand why an order of operations is important doesn'...
This is also true to me. You make good points.
vast rain
you can compute things in parallel on a piece of paper as opposed to sequentially, which would be required of prefix notation
transposition errors are not completely devastating
but both of these things miss the actual point
which is why in the world do you even care
I suggest before trying to prove mathematics wrong with very basic math techniques
you should pick up a book that will teach a few foundational things
maybe pick up an abstract algebra textbook
deep quartz
which is why in the world do you even care
Because I have suffered. Else I do not know.
vast rain
Because I have suffered. Else I do not know.
usually if you suffer at understanding something, don't fight the tide and actually try to understand why it's done
a lot of these things are done for very good reasons
deep quartz
a lot of these things are done for very good reasons
And many others are done for very bad reasons.
vast rain
yeah but not basic stuff like this
deep quartz
So we must discern individually.
deep quartz
yeah but not basic stuff like this
Oh, you'd be surprised how far evil will truly go.
vast rain
it's pretty arrogant to assume that you can discern that certain very elementary mathematics is done badly when it's sufficed for a thousand years
maybe once you've mastered it you can level some critiques at it
but certainly not when you have issues comprehending what the order of operations is
deep quartz
it's pretty arrogant to assume that you can discern that certain very elementary...
It is not that it has been done badly. It is that I believe there exists better. And we all deserve better.
vast rain
It is not that it has been done badly. It is that I believe there exists better....
then understand it completely first
before trying to prove that it's all wrong
deep quartz
then understand it completely first
So you have this complete understanding?
vast rain
of this elementary stuff? pretty near complete
this is all stuff that I was taught in the 6th and 7th grades, so I've had a lot of time to think about it
deep quartz
n + 1 = 1(n + 1) = [1(n + 1)]/1 = n + 1. Is this agreeable to you?
If it is then maybe I am content.
deep quartz
Then maybe it isn't so wrong or bad after all.
vast rain
what isn't
deep quartz
Our math.
vast rain
obviously it isn't
if you ever take a proper engineering class you'll use it all of the time
it's very useful
and people invest LOTS of effort to make formerly complicated things simpler
deep quartz
I flunked out of college my sophomore year, regretfully. But maybe someday lol.
deep quartz
and people invest LOTS of effort to make formerly complicated things simpler
I really enjoy doing that. I could even call that one of my passions in life.
vast rain
yeah well you can't do that unless you understand it yourself
deep quartz
yeah well you can't do that unless you understand it yourself
I think that's what I'm trying to do with all this. Somehow.
vast rain
you shouldn't fight the tide with the presentation of mathematics
obviously trying to put some concepts in your own words and in simpler terms is useful
but you can't go around trying to demonstrate that somehow this equations thing is wrong or whatever
deep quartz
obviously trying to put some concepts in your own words and in simpler terms is ...
Speaking of which, do you know of any good way to visualize taking the root of something mathematically? But like visually/mentally? Lol.
deep quartz
but you can't go around trying to demonstrate that somehow this equations thing ...
I understand.
vast rain
Speaking of which, do you know of any good way to visualize taking the root of s...
many ways
deep quartz
Taking a root seems far less intuitive to me than the other more basic functions.
vast rain
this is finding the root of a polynomial x^n - a
or you can view it on the complex number plane as cutting a rotation
or use logarithms or whatever
look up taking roots of complex numbers
someone will talk about why it's a rotation
deep quartz
look up taking roots of complex numbers
Okay. I will. Thank you.
frail lake
So i barely even understand what this question is asking. To me, it seems like there would be an infinite amount of ordered lists because binary numbers go on forever:
devout snowBOT
So i barely even understand what this question is asking. To me, it seems like t...
stone stump
n is fixed
frail lake
yeah but i dont know what n is
like if n is 3, then only 2 ordered lists will add to an odd number
stone stump
what if n=4?
what if n=5?
n=6?
you want to find some formula which you can plug n into and get the correct number
frail lake
oh so im going to represent the answer with a variable? Not a discrete number?
stone stump
if you want to call it that, sure
frail lake
okay thank you so much for clarifying
devout snowBOT
@frail lake Has your question been resolved?
thin flicker
So, I'm deriving this function (see Image) and I first rewrote it to avoid the product rule, but desmos shows the curve mirrored, if x < 0. Did I do something wrong or is it because desmos always picks the positive output of a sqrt?
devout snowBOT
So, I'm deriving this function (see Image) and I first rewrote it to avoid the p...
violet wind
desmos always picks the positive output since that's how sqrt is formally defined
otherwise it would have 2 outputs for every positive input and wouldn't be a function
that leads to some weirdness in situations like this where we might want a negative final y-value
a*sqrt(b) = sqrt(a^2 * b) doesn't work when a is negative sadly
devout snowBOT
@thin flicker Has your question been resolved?
thin flicker
So could I continue with this function or is there another way, without the product rule?
Im prompted to have the functon for x>0 so Im guessing yes, but if there's another way it would be better
devout snowBOT
@thin flicker Has your question been resolved?
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Available help channel!
paper birch
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jagged schooner
paper birch
sorry
I sent the message by mistake it is incomplete
I'm showing my work now
one second
woven radishBOT
paper birch
hmmm Ok. you gave me an idea I will try to solve it and come back again
half minnow
đź‘Ť
devout snowBOT
@paper birch Has your question been resolved?
paper birch
đź‘Ť
Hi i think this is true. can you confirm?
oh forgot to put the -1 in the very end.
but I simply used the assumption to prove that by adding one more term to the series will equal using n=(k+1) in the equation and thus left equals right
does this make sense
half minnow
yeah that looks good to me
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Available help channel!
fast helm
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fast helm
could i get help for each question
i just need an understanding of what each one is aksing
coral token
i just need an understanding of what each one is aksing
first one
from r draw a north point
and it wants bearing to q
fast helm
wdym by that
coral token
do u know what true bearings r
fast helm
are they just an angle out of 360?
fast helm
yes
coral token
basically how many degrees from north is true bearings
coral token
prolly look on yt or something
spring fractal
i have a bunch of geometry work that i NEED to do, but cant. im just seeing if anyone could help me on it also gonna be on and off afk if anyone would prefer to dm.
devout snowBOT
i have a bunch of geometry work that i NEED to do, but cant. im just seeing if a...
spring fractal
just some of the stuff, not all
marsh agate
Which one then?
spring fractal
Which one then?
all of them, i have more than 10 pages of geometry work.
main gull
all of them, i have more than 10 pages of geometry work.
Yeah.... no one is going to help you with all of that. That takes way too much time. You're better off either asking your teacher for help, getting help from classmates, or looking up resources if you don't know what to do
devout snowBOT
@spring fractal Has your question been resolved?
thin gust
just some of the stuff, not all
HAHAHA nice smiley faces (:
but I can’t help with like every qn HAHA,, maybe 1 or 2? then u can try the rest
thin gust
Yeah.... no one is going to help you with all of that. That takes way too much t...
^^ maybe ask ur teacher and they can help imp ur understanding
spring fractal
HAHAHA nice smiley faces (:
thanks LOL i couldn't stop drawing them
spring fractal
but I can’t help with like every qn HAHA,, maybe 1 or 2? then u can try the rest
alright awesome
devout snowBOT
@spring fractal Has your question been resolved?
tight peak
$\sum_{r=0}^n{\frac{\sin^4(2^r\theta)}{4^r}}$
devout snowBOT
$\sum_{r=0}^n{\frac{\sin^4(2^r\theta)}{4^r}}$
woven radishBOT
Darth Vader
marsh agate
I see geometric sequence
tight peak
Elaborate
It's not sin^r(theta)...
<@&286206848099549185>
What happened to the helpers ping's colour
by any chance am I pinging some dude named helper? 
anyway someone give me any clues to begin this problem with 
please
Fuck
.close
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Available help channel!
restive river
Can mathematical propositions be reduced ?
Eg. I have to prove that
$$X \iff Y$$,
and the way I managed to do it is:
$$X \land A \land B \implies Y$$
$$Y \land A \land B \implies X$$
The problem is that I didn't prove that $X \iff Y$. I proved that they are equivalent if $A \land B$. But this is a requirement for both $X \implies Y$ and $Y \implies X$. Does this mean that $A \land B$ can be reduced, so that we are left with only $X \iff Y$ ? Like you would reduce both terms of a fraction if they have a common divisor.
If I need to state exactly what each of the propositions mentioned are, tell me, and I'll tell you. For the sake of simplicity though, I didn't define them in this question because I think it isn't relevant.
woven radishBOT
trololol !
tiny panther
Reasonably sure you have to show A and B
restive river
Reasonably sure you have to show A and B
Hmm... can I tell you what each of these proposition are ? I have to prove that X <=> Y no matter what, and I'm not sure how I would get rid of the A and B... it might take a while though, since the demonstrations can be long... maybe you can help me find another way to write it so that it doesnt depend on A and B
tiny panther
Sure
restive river
okay
tiny panther
Will see if I can do it
restive river
Will see if I can do it
So, we have two definitions of a bisector:
- A bisector is the line which splits an angle into two equal angles.
- A bisector is the set of points equally distant from both lines of the angle.
We have to prove that they are equivalent.
The way I did it is:
Let $a$ and $b$ be two lines with a common origin named $O$.
Let $c$ be the bisector of $\angle{ab}$.
Let $C$ be any point on $c$.
Let $A \in a$ and $B \in b$ be the perpendicular from C on $a$ and $b$.
Let $def1$ : c is bisector of $\angle{ab} \iff \angle{ca} \equiv \angle{ba}$.
Let $def2$: c is bisector of $\angle{ab} \iff d(C; a) = d(C; b)$
$((def1 \implies \angle COA \equiv COB) \land (CO$ is a common line for $\triangle{COA}$ and $\triangle{COB}) \land (CA \perp AO \land CB \perp BO \implies \triangle{COA}$ and $\triangle{COB}$ are right triangles$)) \implies \triangle{AOB} \equiv \triangle{COB} \implies CA \equiv CB \implies d(C; a) = d(C; b) \implies def2$
woven radishBOT
trololol !
restive river
I did the same for def2 <=> def1 - literally the only thing that changes is that I didnt prove that COA and COB are congruent triangles based on the angle-hypotenuze case, but rather on the cathete-hypotenuze case (idk if i spelled it right)
so the last two conditions (A and B) for the congruency of the triangle are the same
tiny panther
Yes, you prove it this way
restive river
only the first one changed (i started from $def1$ instead of $def2$)
woven radishBOT
trololol !
restive river
Yes, you prove it this way
hmm, but isnt it problematic that def1 isnt the only requirement for the congruency of the triangles, and that it depends on two other conditions too ?
tiny panther
But of the other two conditions
CO being common is true by definition of the triangles you have
And the perpendicularity is from the definition of distance to a line
tiny panther
And the fact this is true is the same as showing A and B
restive river
And the fact this is true is the same as showing A and B
i see
so, since A and B are always true, it means that X <=> Y is always true, no matter what
tiny panther
Yep
Well in the set up of the question; if you were to name things differently or it up differently they wouldn't be
But yes with an angle bisector and the points you gave it is always true
native niche
Do variables matter in finding the GCF of a pair of monomials?
devout snowBOT
Do variables matter in finding the GCF of a pair of monomials?
@native niche Has your question been resolved?
Available help channel!
umbral niche
devout snowBOT
umbral niche
I don't have any idea
pseudo basin
what's a "disjoint number"?
umbral niche
gcd (a,b) = 1
pseudo basin
ok, so that's called coprime
umbral niche
aha
pseudo basin
and what is it that you need to prove?
pseudo basin
oh, so what you mean is:
let a, b, c be integers with gcd(a,b) = 1
prove that if c | (a+b) then gcd(a,c) = 1
do i understand correctly?
pseudo basin
do you have access to bézout's identity
umbral niche
yes
pseudo basin
ok then you have integers x and y s.t. ax + by = 1
and you have an integer k such that a + b = kc
ax + by = a(x-y) + (a+b)y = a(x-y) + cky
devout snowBOT
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Available help channel!
magic thicket
Dirichlet's simulataneous approximation theorem states that
$\forall \alpha_1, ..., \alpha_k \in \mathbb{R}, \forall N \in \mathbb{N}, \exists q \leq N^k, p_1, ..., p_k \in \mathbb{Z}, \forall 1 \leq i \leq k, |q \alpha_i - p_i| \leq \frac1N$
Many sources, such as wikipedia (https://en.wikipedia.org/wiki/Dirichlet's_approximation_theorem) state that it can be proved using the pigeonhole principle, similarly to the single case (k=1), but I don't see how
devout snowBOT
Dirichlet's simulataneous approximation theorem states that
$\forall \alpha_1, ....
woven radishBOT
themateo713
magic thicket
I found many links that mention it but none that actually proved it directly (or used Minkowski's theorem, which isn't my goal)
devout snowBOT
@magic thicket Has your question been resolved?
magic thicket
<@&286206848099549185>
stone stump
instead of dividing the unit interval into N pieces, divide the unit cube [0,1)^k into N^k smaller cubes and consider the vectors of the non-integer parts of the numbers
also let k run from 0 to N^k
magic thicket
if you consider the vectors (xi1, ..., xik) in [0, 1[^k, but only the first N multiples, you get (N+1)^k of them so there's a sub-cube in which 2 vectors fall, right ?
magic thicket
I don't really see what it brings
stone stump
well otherwise you don't have enough vectors
merry hemlock
just some of the stuff, not all
ez
stone stump
you only have N+1 vectors otherwise
you need that two whole vectors are in the same subcube
not only some components
magic thicket
you consider the same multiples together ? I thought it was more of a cartesian product thing
ok
stone stump
we want the same q for all of them
magic thicket
ok I think I get it
I'm gonna try and write that up, I'll come back if I don't manage, but should be ok
thx
.close
midnight dirge
HIIIIIIIIIIII
devout snowBOT
HIIIIIIIIIIII
midnight dirge
for a taylor series of f about c of radius of convergence r(c), can i think of radius of convergence as the neighbourhood about c, some z can take on such that the taylor series gives an estimation of f(z), instead of going to inf
devout snowBOT
@midnight dirge Has your question been resolved?
midnight dirge
ok anw
midnight dirge
so taylor expansion of sin(1/z) is
1/z - 1/(3!z^3) + 1/(5!z^5) -...
arctic field
laurent
arctic field
uh
midnight dirge
pick an annulus?
midnight dirge
ok nvm
arctic field
but should be g
arctic field
lol
midnight dirge
com e back ltr mayb
how do i taylor expansion
like the example i was given is some
1/P(x)
arctic field
you compute derivatives
midnight dirge
where P is a polynomial
arctic field
oh
arctic field
you compute geometric series
arctic field
oh
arctic field
you compute taylor for log
midnight dirge
can we use geometric on f/f'
arctic field
yes
arctic field
:c
midnight dirge
it was weird
arctic field
geometric
midnight dirge
a lot cancelled but no pattern
arctic field
and pray to landau
arctic field
🙏
midnight dirge
@arctic field
NOOOOO
SO
say
i got
f=ln(g)
i got a taylor expansion of f'
arctic field
what happen lol
arctic field
so dramatic
arctic field
LOL
arctic field
🤯
midnight dirge
oh wait it does
arctic field
weierstrass saves the day
midnight dirge
i was so lost
no wonder
it says to reference another lect
n that lect happens to start with
weierstrass safety net
hais
arctic field
i was so lost
but now you're found
midnight dirge
so confused
midnight dirge
by landau
arctic field
like you
arctic field
🙏
atomic vortex
Hello
midnight dirge
if only everyone listens to me and the commands i get from god
arctic field
D:
arctic field
sounds just like normal operations
arctic field
what commerce friends 
midnight dirge
same
arctic field
all my friends are pure math majors /s
midnight dirge
sry
how do i
explain
weierstrass
wasnt 1 of ur friends
a commerce major
that
one doing math
hahhaha
so ive to say
converges uniformly
arctic field
power series converges uniformly
arctic field
then weierstrass double series
midnight dirge
all taylor series r power series
arctic field
or whichever it was
midnight dirge
so i can just say
arctic field
maybe
arctic field
not sure what's proved or not
midnight dirge
pip install packages
midnight dirge
y
arctic field
all my homies hate pip
midnight dirge
what
arctic field
anyway im out
devout snowBOT
Available help channel!
sudden solar
devout snowBOT
devout snowBOT
@sudden solar Has your question been resolved?
fresh cairn
can a region R be both open and bounded
devout snowBOT
can a region R be both open and bounded
stone stump
yes
fresh cairn
hmm
stone stump
for example (0,1) is open and bounded because it's contained in the disc (-2, 2) of radius 2
fresh cairn
as opposed to [0,1]?
next cypress
I got 2 vectors, and I have to find the sinus of the angle between them. They gave me the coordinates of the vectors. I’m stuck after calculating |A| and |B|, and A . B (A and B are the vectors)
devout snowBOT
I got 2 vectors, and I have to find the sinus of the angle between them. They ga...
last swan
Do you know how you can express the dot product of two vectors in terms of the angle between them?
next cypress
I can show you where I’m stuck at
next cypress
Do you know how you can express the dot product of two vectors in terms of the a...
Yea
It’s pretty messy
last swan
Hmm yeah on second thought it might be better if you use the coordinate notation approach of calculating the cross product as described here: https://en.wikipedia.org/wiki/Cross_product
And then divide it by |A||B|
next cypress
Alright, I’ll take a look at it
Oh yeah, I forgot to mention the vectors are on a cartesian coordinate system
last swan
Yeah that’s fine, were you able to calculate the cross product?
next cypress
I haven’t, I don’t really know which of the formulas I gotta use
last swan
Hmm did they cover how to calculate cross product for 2d vector using coordinates?
ignore the k, as the cross product is perpendicular to the plane of both vectors
If you divide that by the product of the magnitudes of both vectors that should give you the sine of the angle between them
Hopefully that page makes it clear why that’s the case
echo field
echo field
<@&286206848099549185>
jade atlas
simplify and try rationalizing
for first 3 options
do uk how to do that
for making things easier
try writing sqrt(8) as 2sqrt(2)
and sqrt(18) as 3sqrt(2)
plush cave
The last question is fucking with me, how is -X, 1 wrong and how do I find the correct answer?
devout snowBOT
The last question is fucking with me, how is -X, 1 wrong and how do I find the c...
@plush cave Has your question been resolved?
plush cave
.close
vestal notch
devout snowBOT
vestal notch
Answer key says answer is 1.2 * 10^6 6 for first question
But i don't understand how
I did distance = speed * time = 40 * 3 = 120 km and then multiply by 1000
120000
keen wren
you're correct
restive river
devout snowBOT
restive river
what the hell happened here
wooden veldt
i dont speak that language but it clearly says "if the quotient is equal to 0, then the numerator is equal to zero"
wooden veldt
$\frac{a}{b} = 0 \implies a = 0$
woven radishBOT
ÎŁAC
wooden veldt
(if b isnt 0)
ember ether
somone german?
devout snowBOT
somone german?
exotic stump
nein
devout snowBOT
@ember ether Has your question been resolved?
toxic orbit
somone german?
Yes I'm german
wary dove
How can I calculate the Maximum value of an equation? I don't know that much about Limits and Derivatives
devout snowBOT
How can I calculate the Maximum value of an equation? I don't know that much abo...
wary dove
def HorrificEquation(self: GameState) -> float:
wallet = self.wallet # This is different at every call
total_rounds = self.rounds # This is a constant
remaining_rounds = self.rounds - self.current_round # this is different at every call
map_gold_count = self.map.gold_count # This is a constant
if wallet > map_gold_count * 2: # This caps the maximum value of wallet
wallet = map_gold_count * 2
up = total_rounds * wallet
down = remaining_rounds * map_gold_count
Some = up / down
All = 1 # code to calculate the maximum possible value of (up / down)
return percent(All, Some)
I want to return a value that is always in a fixed range (0,100)
But to be able to do that I need to know what is the maximum possible value of my equation
which is
Some = (total_rounds * wallet) / (remaining_rounds * map_gold_count)
wallet is always a positive number and between 0 and map_gold_count*2
total_rounds and map_gold_count are always positive numbers and always have the same value
remaining_rounds is a number between 1 and total_rounds
solemn fox
I want to return a value that is always in a fixed range (0,100)
so is this like a percentile in between the min and max?
wary dove
so is this like a percentile in between the min and max?
Yea exactly
I know I should use limits because this isn't a linear equation, but the thing is I know nothing about Limits and Derivatives
solemn fox
yeah, I've only gotten to limits as of yet
wary dove
yeah, I've only gotten to limits as of yet
So no help?
wary dove
right so you got some bython code
yea br0
restive chasm
oh
wary dove
The code is not of importance here
wary dove
I just need to know how to now the maximum possible value ( Which I believe must be measured by limits)
restive chasm
right but what kind of equation/function are we talking
wary dove
polynomial?
Oh yes
wary dove
```python
def HorrificEquation(self: GameState) -> float:
wallet = self.wal...
Here
up = total_rounds * wallet
down = remaining_rounds * map_gold_count
Some = up / down
Here I explained about the variables here
wary dove
I know how to do this in math
Really?
My savior!
scarlet peak
You don't need limits I don't think
solemn fox
I don't really understand the math you're doing.
restive chasm
You don't need limits I don't think
if you want to use derivatives though
solemn fox
multiplying the total_rounds by wallet is weird
wouldn't the max wallet score by the end just be the map_gold_count?
restive chasm
I don't really understand the math you're doing.
I don't either but apparently want's to find global maxima for polynomial
wary dove
Am I wrong somewhere?
restive chasm
So derivatives are usually defined in terms of limits
wary dove
Is it possible to calculate the maximum possible value of (up/down) ?
knowing which elements are variables and which are constants
I even specified the range of the variables
solemn fox
well it depends on the bounds of wallet
wary dove
well it depends on the bounds of `wallet`
It's between 0 and map_gold_count * 2
scarlet peak
Right, total rounds = map gold I'll call them x
Wallet is between 0 and 2x
Rounds remaining between 1 and x
The maximum value of a fraction occurs when thr top is as big as possible and the bottom is as small as possible
solemn fox
then the max would just be
$\frac{map_gold_count*wallet}{total_rounds * map_gound_count}$
I think
woven radishBOT
Carter
solemn fox
oops sorry for interjection didn't see the new messages
wary dove
So there is no need for Limits?
solemn fox
the min would be 0 because wallet could be 0
wary dove
Yes and the max?
solemn fox
**Carter**
this
scarlet peak
Therefore I'll pick the biggest on the top and smallest on the bottom
For total rounds,I chose between 1 and x. Total rounds is on the top therefore I chose x
Wallet is between 0 and 2x, on the top therefore I chose 2x
Remaining rounds between 1 and x, on bottom therefore I pick 1,
Map gold is x therefore I pick x
So my fraction is
wary dove
Hmm
scarlet peak
This cancellation to 2x
wary dove
let me thing about it
scarlet peak
Therefore the maxis thr wallet
wary dove
(total_rounds * map_gold_count * 2) / ( 1 * map_gold_count)
@scarlet peak
does this seem legit?
scarlet peak
For what?
wary dove
Oh bad use of word legit
Is that the maximum possible value?
According to your explanations
Biggest on the top
and the smallest on the bottom
scarlet peak
Yeh that's what you said earlier that wallet is 2x that
wary dove
Yeh that's what you said earlier that wallet is 2x that
Thank You! 
scarlet peak
I'm curious what are you making
wary dove
I'm curious what are you making
Ah okay
scarlet peak
You're welcome
scarlet peak
I mean I don't see why not🤣
wary dove
Okay then
You see those ships?
they should collect coins
and retrieve them to the treasuries in the center
The maximum amount of golds is determined in the initialization state of the game
and the game goes on for example 100 times
that's the total rounds number
I'm making an AI that aims to retrieve the golds it collected at the best time
That's the equation you helped me with
scarlet peak
That's a cool project
wary dove
It's an ongoing tournament , but me and my colleague were stuck on this formula
So I asked
scarlet peak
đź‘Ť
scenic coral
help?
scarlet peak
How many miles did they do
scenic coral
How many miles did they do
I have to figure that out before answering the actual question?
scarlet peak
What do you mean
Yeh, miles per gallon requires you to know the number of miles and gallons
scenic coral
Yeh, miles per gallon requires you to know the number of miles and gallons
oh goodness, im not sure
scarlet peak
So you stop and fill your car. Your car says its done 19874.5 miles in its life. You carry on driving and you stop again, and it says 20105.5 miles
How many miles have you travelled
scenic coral
So you stop and fill your car. Your car says its done 19874.5 miles in its life....
231?
scarlet peak
Miles per gallon is how many miles you do for every 1 gallon
You've got the miles for every 17.5
scenic coral
Do I multiply?
scenic coral
Im not sure 
scenic coral
$2 ?
scarlet peak
Well done
Now use that same logic 17.5 gallons gets you 231 miles
How many miles does 1 gallon get
scenic coral
Thank you for your help and patience (: !
scarlet peak
No worries đź‘Ť
scenic coral
.close
vernal anvil
Would anyone be able to help me understand this question
devout snowBOT
Would anyone be able to help me understand this question
neat apex
do you know the Triangle Inequality?
neat apex
can you write it here, so we can look at it together?
vernal anvil
I can type what i understand
so I know the inequalities both both sides of the triangle
and knowing that they both are less than 0.01 and 0.04 respectively
following the rule, the combined values must be less than those 2 values combined
i am just not sure how to show it
neat apex
great, can you write the formula for Triangle Inequality?
vernal anvil
|a+b|<|a|+|b|
neat apex
cool
vernal anvil
where a is the x inequality and b is the y inequality
and |a| and |b| would be the other sides of the inequalities
neat apex
do you see, how can we rewrite |(x+y)-5|?
neat apex
not clear for me - can you restate?
vernal anvil
this what I have
however it felt wrong to change the <= to just <
i dont have a reason for why i did it
vernal anvil
sure
neat apex
do you see, how can we rewrite |(x+y)-5|?
neat apex
can you rewrite it in terms of x-2 and x-3?
vernal anvil
it is <0.05
not <=
but i think that is because of the inequalities listed previously
could i use the previous inequalites to say that |a|<0.01 and |b|<0.04
neat apex
Ok, I fix it
neat apex
wait, wait
so we have
|x-2|<0.01
|y-3|<0.04
and we should prove that
|(x-2)+(y-3)| <0.05
ok?
neat apex
I propose to rename some expressions in terms of a and b, ok?
so we have
|x-2|<0.01
|y-3|<0.04
and we should prove that
|(x-2)+(y-3)| <0.05
neat apex
can you see what are a=?, b=?
neat apex
great
vernal anvil
i see
so then
|a+b|
which is now
|(x+y)-5|
is now the inequalities listed previously
i see
neat apex
that's it
neat apex
thank you
devout snowBOT
devout snowBOT
Available help channel!
quartz linden
devout snowBOT
quartz linden
Could someone please help me with this?
devout snowBOT
@quartz linden Has your question been resolved?
granite marten
where did they get the k from?
devout snowBOT
where did they get the k from?
granite marten
i understand that for i, you would get (1 + 0) = 1i, or i
and that for j you would get 0 times e^-0 = 0j
but for k wouldnt you get sin (0) / 0 = undefined?
solemn fox
but for k wouldnt you get sin (0) / 0 = undefined?
that is an identity
$\lim_{x \to 0} \frac{sin(x)}{x}=1$
woven radishBOT
Carter
granite marten
if x were to equal 2 would it still be 1?
solemn fox
iirc uses the squeezing theorem
granite marten
since 2 is outside of the potential value range for sin?
solemn fox
since 2 is outside of the potential value range for sin?
sin takes values larger than 2pi, they just wrap around
solemn fox
yes, if it fits that theorem
granite marten
oh wait identities in general are always true correct
solemn fox
solemn fox
oh wait identities in general are always true correct
yes
they list the constraints if there are any constraints
granite marten
.close
twilit estuary
how do i make y=2x^2-4x+7 into vertex form
devout snowBOT
how do i make y=2x^2-4x+7 into vertex form
neat apex
do you know how to complete the square?
twilit estuary
i tried completing it and failed
twilit estuary
do you know how to complete the square?
so no
twilit estuary
yes
hybrid snow
so you would have $2\left(x^{2}-2x+\frac{7}{2}\right)$
woven radishBOT
Umbraleviathan
hybrid snow
you would complete the square on $x^{2}-2x+\frac{7}{2}$
woven radishBOT
Umbraleviathan
twilit estuary
thats complete?
twilit estuary
what do i do after that
hybrid snow
distribute the 1/2
hybrid snow
what do i do after that
what did you get after you completed the square
hybrid snow
**Umbraleviathan**
on this part
twilit estuary
isnt it easier when we factor out 2 to keep put 7 out of it?
hybrid snow
no you have to include the 7
hybrid snow
**Umbraleviathan**
so this
and all you gotta do is complete the square on x^2 - 2x + 7/2
which i asked, "what did you get after you complete the square", which hasnt been answered
twilit estuary
u split 2x in half?
hybrid snow
you can
i mean
you split the coefficient of 2x in half
then square the coeffient
but like if im gonna be honest
x^2 - 2x + 1 is a perfect square polynomial @twilit estuary
7/2 = 1 + 5/2
so its gonna be (x-1)^2 + 5/2
but then you have to distribute 2 into it
because we factored 2 out
twilit estuary
yea
twilit estuary
x^2 - 2x + 1 is a perfect square polynomial <@743164374432219165>
where did +1 come from
hybrid snow
where did +1 come from
(-2/2)^2
devout snowBOT
@twilit estuary Has your question been resolved?
twilit estuary
im still so confused
raw knoll
devout snowBOT
lunar harbor
hybrid snow
It wants ln, not e raised to the
raw knoll
this is what i wrote on paper
i know log base e of 8 is just in8
just confused what to do after
hybrid snow
There's a couple way do this
You can use log power-base rule
Where $\log_{a^b}(A) = \frac{1}{b} \log_{a}(A)$
woven radishBOT
Umbraleviathan
hybrid snow
So essentially $e^b = 8$
woven radishBOT
Umbraleviathan
hybrid snow
And you find b
Which should be obvious that b = ln(8)
So $\frac{1}{\ln(8)}\ln(x^2+6)$
woven radishBOT
Umbraleviathan
hybrid snow
https://www.desmos.com/calculator/wvwijfmvx9 you can see its the same function, just with base e @raw knoll
