associates?
#general discussion
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hollow ice
2y degree
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oh
hollow ice
AS is a 2y degree
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im so bad at english 
hollow ice
not 4y
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i didnt actually learn english formally, i gained 90% of my skills mostly by talking a lot on discord
agile roost
AS is a 2y degree
ASS degree
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this is the education liberals want
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what is neek
agile roost
idk the formal definition
hollow ice
humiliate me more daddy
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hot
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lmao
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,w neek definition
vivid gulchBOT
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ah
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nothing
hollow ice
yes exactly
agile roost
I have the message log 🙂
hollow ice
FUCK
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oh right lmao
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if magma's maths is acceptional, what is mine 😭
agile roost
if magma's maths is acceptional, what is mine 😭
unacceptional
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hollow ice
yes
hollow ice
$x^2 - 1 = 0$
vivid gulchBOT
Magma <3 (SL_2(R) Group)
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yeahhhh
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**Magma <3 (SL\_2(R) Group)**
D = 0^2 - 4*1*(-1) = 4
x = (0 +- sqrt(2))/2 = +-1
my english listening skills allows me to understand only 60% of this conversation
@hollow ice also what did you want to say?
hollow ice
🥵
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k
im back
i have no idea whats the conversation about
i have sent enough information in this conversation to get doxxed, but its so hard its near impossible
guys do you use 12-hour format or 24-hour format
if you use 24 hour format you are based
normal arrow
speaking of mental maths, i once derived an approximation of Lambert W-function using the uhhh
quadratics and intervals
W0(x) = (log2(x) - n + 0.9355)/(2^(-n) + 1.443)
im going to sit here just to listen to magma's voice
alright
hollow ice
I preferred you belittling me :(((((
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W0(x) = (log2(x) - n + 0.9355)/(2^(-n) + 1.443)
im going to make a desmos demo with this so Magma-kun can notice me 🥺
hollow ice
im going to make a desmos demo with this so Magma-kun can notice me 🥺
I will :)
hollow ice
Continually pushing myself into depravity, I will inform you that you have never had an original thought in your life. Your life is pointless, you should just end it now @agile roost .
agile roost
Be original. Use your fucking brain for once in your entire miserable existence. I mean seriously, you're over a decade old and have achieved nothing of note, get your shit together. There are 5 year olds in this world who have progressed their field further than you and endured greater hardships than you. There are dead people with more bitches than you and prostitutes with more dignity than you. Get a fucking life, pull your miserable and worthless existence out of the rut of self pity that you have plunged yourself into for the last years. It's honestly pathetic; you're the future of this planet and you have already disappointed everyone you've ever known. Get your shit together.
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obv
hollow ice
John Math probably has the most amazing Russian accent ever
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and my english pronunciation is really meh
and i cant spell L and R
as well as th
so you tell me
versed comet
I wanted to make a math riddle but I'm too dumb dumb to make a good one because I'm only in my 2nd year of A-Levels and these riddles look like university level stuff
@dusty swallow how do we nominate someone for idiot of the week
dusty swallow
Just dm me
ancient helm
You have to give a minimum 100 word essay to dappy about why said person sucks and deserves idiot of the week
dusty swallow
Yes
normal arrow
why am i not the permanent idiot of the week
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lmao
vague dagger
.m rule 1
latent marshBOT
dusty swallow
It’s not toxic
Everyone loves it
What if I make a petition?
There has to be a way to make idiot of the week an actual thing and make sure I don’t get banned next week
ancient helm
There has to be a way to make idiot of the week an actual thing and make sure I ...
If you become the server owner, you can do anything you desire
dusty swallow
@open whale see this
After my application to manager failed
I will gladly become server owner
dusty swallow
Just read some of the messages
So u see the new format I tried in #maths-riddles ?
Idiot of the week namely
It’s a hit
But eph isn’t so on board with it
dusty swallow
If you become the server owner, you can do anything you desire
Luckily doubleG had a great idea
ancient helm
DAM IT NOW IM NOT EVER GONNA GET IDIOT OF THE WEEK
open whale
i need my nitro dappy
dusty swallow
@agile roost look at this
dusty swallow
i need my nitro dappy
Real
ancient helm
Discord mods when they don’t got nitro
(Their entire soul is from the ability to post custom emojis on discord)
dusty swallow
Yoav gets payed in nitro/minute
ancient helm
I get paid in not so fresh air
dusty swallow
Impressive
agile roost
i need my nitro dappy
free nitro????
agile roost
dusty swallow
Alex
agile roost
free nitro for me
ancient helm
Managers of partnered servers get free nitro
Think it’s only the owner
ancient helm
Bet
hollow ice
Here, @ashen agate
Canis is not ever going to show himself he was humiliated so badly twice in a row
ashen agate
Ignore dumbassery
hollow ice
You should've seen how he treated some people earlier
ashen agate
Put them in their place
dusty swallow
He was a pretentious a—hole
Just like me
hollow ice
No you are fine (unironically) compared to this kid.
dusty swallow
What is ur guys fav Star Wars film
hollow ice
Fuck you dappy
dusty swallow
What is ur guys fav Star Wars film
Very important
hollow ice
I will arrive there in 20 minutes tops
sharp nexus
saw that
dusty swallow
Math Duell
dusty swallow
I’m still waiting on ur responses
ashen agate
Just send location
hollow ice
I will give you irreducible Galois polynomial of order 5
dusty swallow
U better not tell me u guys didn’t watch Star Wars
dusty swallow
I will give you irreducible Galois polynomial of order 5
Nice
Not how it works buddy
U have to solve it urself
So u can give it as a question
ashen agate
Next riddle: exact roots of quintic polynomial
hollow ice
Yes exactly
hollow ice
U have to solve it urself
Fine
I will pick impossible polynomial to solve
Stupid nested roots
10,000 nested roots
ashen agate
This is a fun idea for a programming puzzle
ashen agate
You make a polynomial and you have to guess and check all sorts of crazy expressions
hollow ice
Maple isn't open-source
ashen agate
With square roots and stuff
You give a general guideline of what the roots look like
hollow ice
Hmm. How about what is the highest order of a polynomial that can be solved with nested radicals of length $n$?
vivid gulchBOT
Magma <3 (SL_2(R) Group)
hollow ice
Such that the nesting does not evaluate to $1$ or $0$.
vivid gulchBOT
Magma <3 (SL_2(R) Group)
ashen agate
7
ashen agate
8?
hollow ice
no
For a closed form it is 5
For a general solution it is infinity
Boringly
Because
Consider a polynomial $x^2 - 2 = 0$
vivid gulchBOT
Magma <3 (SL_2(R) Group)
hollow ice
Has depth $1$ for solution
vivid gulchBOT
Magma <3 (SL_2(R) Group)
hollow ice
Now choose $x^{10000} - 2x^{9999} = 0$
vivid gulchBOT
Magma <3 (SL_2(R) Group)
ashen agate
So you agree that it is 7
hollow ice
More specifically, what about a polynomial that has all solutions that are irreducible in the nesting of the radicals for all solutions
I.e. there exists a polynomial like that
hollow ice
Hmm, I doubt it.
ashen agate
OK I'll stop
ashen agate
Oh
vivid gulchBOT
Magma <3 (SL_2(R) Group)
hollow ice
If I had to guess
ashen agate
So 7 works in a way
hollow ice
Like for quadratics we have polynomials say with roots $\frac{1 \pm \sqrt5}{2}$
vivid gulchBOT
Magma <3 (SL_2(R) Group)
hollow ice
And I wonder about $1 + \sqrt{1 \pm \sqrt[3]{5}}$
vivid gulchBOT
Magma <3 (SL_2(R) Group)
hollow ice
Maybe there is a cubic like this
ashen agate
Mahbe
hollow ice
I can check
Nope
2 nested is 6
I see
You need waaaaay more PM
I guess it is 2n choose (2n-1)
worn bison
Yes now I can
subtle jacinth
hello everyone
crude plume
vivid gulchBOT
TimeChan
calm ginkgo
Off
normal arrow
no
ancient helm
Just no
dusty swallow
yes
vivid gulchBOT
Professor mid. FRS CBE
ancient helm
Geometric series with a common ratio of 0/0
agile roost
Geometric series with a common ratio of 0/0
based on just those sums it's not just indeterminate, it's undefined
eternal verge
**TimeChan**
Wait wut?
eternal verge
$1+\sum_{n=1}^{\infty} 0 = \sum_{n=0}^{\infty} 0$
Wait why?
hollow ice
hasn't it <@995223500686118942>
Yes 100%
eternal verge
that's also been recently proven
Wut do you mean by "recently?"
agile roost
it was proven by Adolf Hitler
basically your uncle
hollow ice
basically your uncle
yes
agile roost
his maths thesis was done in the margin of mein kampf
hollow ice
his maths thesis was done in the margin of mein kampf
yes
agile roost
flexing on Feynman
eternal verge
earlier this evening
Wut timezone is dis?
eternal verge
it was proven by Adolf Hitler
I thought he was dead?
hollow ice
I thought he was dead?
No, he is living in Argentina
eternal verge
No, he is living in Argentina
So he's well over 134 years old by now?
hollow ice
So he's well over 134 years old by now?
Yes, he is amazing
agile roost
So he's well over 134 years old by now?
oldest man on earth by far
I have a peace of his pink mist in my freezer
tight lagoon
Is that purple curve considered a Parabola? I think not. It is the set of centers of all circles which touch a fixed line and a fixed circle (instead of a point, which was the case for a parabola)
I have found its equation to be
frail vergeBOT
Rendering failed. Check your code. You may edit your existing message.
Error Log:
Missing } inserted.
<inserted text>
}
l.94 \end{gather*}
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.
@tight lagoon 
frail vergeBOT
Rendering failed. Check your code. You may edit your existing message.
Error Log:
Missing } inserted.
<inserted text>
}
l.94 \end{gather*}
I've inserted something that you may have forgotten.
(See the <inserted text> above.)
With luck, this will get me unwedged. But if you
really didn't forget anything, try typing `2' now; then
my insertion and my current dilemma will both disappear.
Shape 2 isn’t a parabola
tight lagoon
Shape 2 isn’t a parabola
That's what I thought thanks for confirming.
This is it's equation
loud lakeBOT
@tight lagoon has given 1 rep to @hollow ice
hollow ice
It’s fine
sour sinew
Is that purple curve considered a Parabola? I think not. It is the set of center...
yes it is a parabola
touching the fixed circle means the distance from the centre to the centre of the fixed circle is r higher which means the line would need to be r further away to make the normal parabola generation algorithm generate it
or,
without loss of generality we can set the line as y = 0,
circle as whatever, yk, x^2 + (y - h)^2 = 1
then r = distance from circle to line is y
and to be tangent to the circle, distance from (0,h) would need to be 1 more than the radius, aka 1 + y
1 + y = sqrt(x^2 + (y-h)^2)
1 + y^2 = x^2 + y^2 - 2yh + h^2
1 - x^2 - h^2 = -2yh
tight lagoon
without loss of generality we can set the line as y = 0,
circle as whatever, yk,...
I am completely lost here. Could you please tell what you're trying to find or prove?
sour sinew
I am completely lost here. Could you please tell what you're trying to find or p...
that the curve is a parabola
tight lagoon
that the curve is a parabola
Ok so I think you've taken the radius as one and the fixed line as the X axis
Then what have you done ahead?
tight lagoon
i should have specified what the a and r are. Then fixed line is at y=-a and the radius of fixed circle is r
My bad
sour sinew
Ok so I think you've taken the radius as one and the fixed line as the X axis
im saying, (say for sake of argument that the line is horizontal and the circle is above it)
if you move the line down by r units, and replace the circle with a point, then the parabola obtained from that is the same as the curve you got
so it has to be a parabola
because increasing the radius of your circle by r would make it go through the point and be tangent to a line r units lower
sour sinew
Shape 2 isn’t a parabola
idk what magma was on
tight lagoon
im saying, (say for sake of argument that the line is horizontal and the circle ...
r units from the center?
sour sinew
wha
tight lagoon
What is r?
tight lagoon
Alright so you're going with that convention
tight lagoon
Yes
sour sinew
well increasing the radius of the moving circle by r
makes it go through the centre of the fixed one, and be tangent to a lower line
and the locus of those centres is a parabola
tight lagoon
Ohhhhhh
I get your point
Very nice argument. Reminds of that trick of contracting and expanding circles which is very helpful in straight edge and compass construction.
sour sinew
interesting
tight lagoon
It is quite similar. For eg You have been given two intersecting lines and a point. You are required to construct a circle passing through that point and touching those two lines. Suppose we already know that. (I will not give its proof here). Now instead of a point you have been given a circle with radius R. So how can we construct? We do what you did while proving that curve was a parabola! You draw two more lines parallel(outside) to the lines already given at a distance of R(like what you did with that fixed line in the parabola case). Now the circle which passes through the center of the fixed circle will have the same center as that of the circle which we desire.
And we know how to construct a circle passing through a point and tangent to those two lines
sour sinew
nice
sour sinew
should a constant function be considered an elementary function if no closed form exists for the constant
open whale
should a constant function be considered an elementary function if no closed for...
no, all constant functions are elementary
it is a nonelementary constant though
sour sinew
no, all constant functions are elementary
wait so it should be considered elementary
i see
frigid hollow
The channel i have veen looking for
sour sinew
if the existence of some object is undecidable and there’s some algorithm to determine whether something fits the criteria required then doesn’t that just mean the object doesn’t exist because if it did you could find it
does that mean undecidability implies lack of algorithm
ancient helm
So basically:
-You can’t determine if an object O exist
-You have an algorithm or method of deciding if some object is O
-Therefore O must not exist as otherwise, your algorithm would’ve said O exists?
dusty swallow
So basically:
-You can’t determine if an object O exist
-You have an algorithm o...
It’s basically “this is a lie” on crack
sour sinew
So basically:
-You can’t determine if an object O exist
-You have an algorithm o...
otherwise there is something you can put into the algorithm and it would say this is O
which would determine it
ancient helm
which would determine it
Did you put every object that could exist into your algorithm
sour sinew
Did you put every object that could exist into your algorithm
no, but if there is one, the algorithm would say yes, which would determine it
but it's impossible to determine it
dusty swallow
I believe Zfn to have taken a good portion of the funny white stuff
ancient helm
no, but if there is one, the algorithm would say yes, which would determine it
Why would it say yes?
Say the set of all objects is called S
Now you only scan S’, a subset of S
If it results yes for any element of S’ then the object must exist
If it doesn’t, then one of two things are true
O is in S-S’ (the set of all elements you don’t scan) and O exists
O is not in S-S’ and doesn’t exist
If you could access the entirety of S, then you can determine if O exists or not
dusty swallow
Ye ok double g definitely took some too
sour sinew
no, but if there is one, the algorithm would say yes, which would determine it
this is what I'm saying
like, if the riemann hypothesis is undecidable, there can't be any counterexample, as that would prove it one way or the other
frigid hollow
Is it sound to assert this infinite sum tends to 0? Or is it indeterminate because of the distinct values the sum produces before n is a multiple of 4 (which marks the annihilation of all previous terms when n is an integer multiple at 4 )
agile roost
indeterminate
doesn't converge on any one value
(1+i)-(1+i)+(1+i)-(1+i), doesn't converge because grouping makes it essentially 1-1+1-1+1... which obviously doesn't converge
(grouping a divergent sum is a no no!!!)
which means that reason is moot, but you see what I'm getting at
frigid hollow
(1+i)-(1+i)+(1+i)-(1+i), doesn't converge because grouping makes it essentially ...
i have seen alot of people assert this is 1/2 because it is always either 1 or 0 but that logic never made sense to me
the average of 2 possible resulting values of an infinite sum doesn't describe the sum at any point even approaching infinity
agile roost
i have seen alot of people assert this is 1/2 because it is always either 1 or 0...
it's an oscillatory series, you can define it to be 0.5 if you want, but it isn't.
frigid hollow
yeah makes sense
agile roost
yeah makes sense
there are different ways that you can derive value from divergent things, for example with integrals that have a discontinuity in the centre of the bounds you can assign a Cauchy principal value
in any case the Cesaro sum of grandis series (1-1+1-1+1-1...) is ½
frigid hollow
cauchy name
frigid hollow
in any case the Cesaro sum of grandis series (1-1+1-1+1-1...) is ½
wouldnt that be 1.5
cuz it only oscillates between 1 and 2
sour sinew
Is it sound to assert this infinite sum tends to 0? Or is it indeterminate becau...
well |i| is not less than 1 so you can predict that it will diverge
agile roost
well |i| is not less than 1 so you can predict that it will diverge
conditional convergence 
(it still diverges)
but the ratio test is inconclusive
frigid hollow
hmm
i have question about inequalities from all this
if a^2>b^2 , what does that tell about the relationship between a and b?
can we assume a>b or do we add plus minus somewhere
agile roost
0>b²-a²
0>(b-a)(b+a)
you do the rest
frigid hollow
but like if we choose to divide 0 by (b-a) then we end up with -a>b
if we divide 0 by (b+a) we get a>b
oh
agile roost
that's why you shouldn't eliminate solutions
agile roost
dividing 0 by them is
versed comet
I need help with a problem
I have no clue where to start nor what the right answer is
frigid hollow
how else would i isolate the b and a to get the relationship between a and b?
oh
can we say |a|>|b|
agile roost
nah
frigid hollow
?
agile roost
square rooting both sides and using the definition of absolute value for real a,b yeah
versed comet
@agile roost mind solving a problem for me
agile roost
what is it
frigid hollow
square rooting both sides and using the definition of absolute value for real a,...
i was about to get confused but you saying "for real a and b" cleared it up XD
agile roost
i was about to get confused but you saying "for real a and b" cleared it up XD
for imaginary a,b you get back whatever you put in 💀
frigid hollow
agile roost
you can safely assume a,b are real as the notion of ordering in the complex plane is not widely defined
refer to what I just said
frigid hollow
basically if 1>-1, and so 1^2>i^2 , i thought id implement the |a|>|b| relation but that clearly won't work for complex a,b
cuz then you can show 1>1 XD
agile roost
you can safely assume a,b are real as the notion of ordering in the complex plan...
here
squaring a value does not guarantee a real output, therefore you wouldn't really be able to generalise a²>b² for complex a,b without additional fiddling
frigid hollow
but why does that matter if a and b are defined on the same domain
agile roost
wdym
frigid hollow
squaring a value doesn't guarantee a real output, but if a and b were both complex it shouldn't matter right?
agile roost
no it will definitely matter
agile roost
as I've reiterated several times
frigid hollow
nvm
agile roost
the complex plane isn't ordered
agile roost
inequalities for z>w are not defined for any complex z,w
there is no accepted way to define inequalities in the complex plane
which is why you get modulus(z)>modulus(w) or whatnot
3+2i>4-3i makes no sense for example
frigid hollow
ohhh nvm i always thought you could define z>w but then follow it up with sqrt(zz#)>sqrt(ww#)
z# being conjugate of z and same for w
frigid hollow
yeah but if i did z*z and then w that symbol w discord removes both
agile roost
yeah
frigid hollow
XD
vivid gulchBOT
PDF File (apex predator)
agile roost
have to be careful with defs
frigid hollow
yeee
i made the mistake of also assuming since modulus(z) converts z from complex to real you can just compare it with reals too
but you cannot compare it after removing the modulus
vivid gulchBOT
PDF File (apex predator)
agile roost
but you cannot compare it after removing the modulus
there is no inverse operation to modulus
so nothing to apply to both sides as to keep the inequality
good night
frigid hollow
Gn
dusty swallow
there is no inverse operation to modulus
Lmao
frigid hollow
there is no inverse operation to modulus
wrong, there is an inverse operation but it's not a function
f(x) = ±x is technically the inverse operation but again, not a function as it cannot be compared on a continuous domain like the real numbers
dusty swallow
Ur gonna give back an infinite amount of numbers
dusty swallow
At that point I can also just give u R and say it somewhere in there 
frigid hollow
not really
dusty swallow
No I mean for inverse mod
frigid hollow
huh
frigid hollow
At that point I can also just give u R and say it somewhere in there <:hahayes:8...
again not really because you can still get back a possible input x for abs(x) when you plug in ±x
unlike saying "the x is somewhere in R"
XD
dusty swallow
If I ask u which numbers give back 2 mod 3
frigid hollow
he said modulus not modulo
know your math
lol
modulo and modulus isn't the same dapz cmon now
frigid hollow
@sand sentinel this is how f resistance is difference in KE and GPE divided by distance
The very first line comes from W=F*D
And so we see although joule isn’t N/m, a newton is joule/m
Also to derive quickly how the delta pe turns negative, resort to PE = mgh and make g negative (-g)as there is a downward acceleration on earth, cheers.
agile roost
wrong, there is an inverse operation but it's not a function
no, that's absolute value
you're using the definition √x²
dappy is right in that mod will give you infinitely many values for a given arcmod or whatnot
you'll have |z|=modulus
so an entire circle of possible values, hence no real inverse operation to recover your input
frigid hollow
I was never talking about modulo 😭
agile roost
I'm not talking about modulo either
frigid hollow
so an entire circle of possible values, hence no real inverse operation to recov...
You mean for complex absolute values?
frigid hollow
Yeah i was talking about real numbers strictly i should have mentioned
Ohhhhhhh
i did not know that
I thought
Modulus and abs
Are interchangable and mean the same thing
Nvm 💀
agile roost
they do the same thing in reals
frigid hollow
But clearly yeah for complex its more defined when using modulus
agile roost
Yeah i was talking about real numbers strictly i should have mentioned
then you shouldn't have said I was incorrect, the message I responded to was you talking about complex values
"removing the modulus"
is not possible with complex values
frigid hollow
then you shouldn't have said I was incorrect, the message I responded to was you...
I wouldn’t have said you’re incorrect if i knew abs(x) and modulus(x) was not interchangeable 💀
I see
frigid hollow
I wouldn’t have said you’re incorrect if i knew abs(x) and modulus(x) was not in...
Yeah sorry i should have looked it up
but like
You were still correct in a way
The reason i pounced and said “incorrect” was because you used the word operation instead of function
(Talking about abs(x))
Abs(x) has no inverse function
agile roost
to which I'm still correct, with abs it's obvious that there is an inverse operation
modulus is the complex expansion of abs, in a way abs has a circle radius |x|
frigid hollow
to which I'm still correct, with abs it's obvious that there is an inverse opera...
Yes as i was saying😂 i didnt know +- x wasn’t a well defined function cuz its continuous
Like those kinda functions are cool
Even (x^x)
frigid hollow
When x is both 0.5 and 0.25 you get the same output which is so cool
agile roost
When x is both 0.5 and 0.25 you get the same output which is so cool
well you can get a similar thing with quadratics, cubics, whatever
frigid hollow
Squareroot(0.5) = 4throot(0.25)
agile roost
it's having different outputs for the same inputs that makes them analytically interesting
frigid hollow
well you can get a similar thing with quadratics, cubics, whatever
Yeah but its less interesting because in quadratics you get the same result but negative for the other solution
Whereas here
agile roost
Yeah but its less interesting because in quadratics you get the same result but ...
x²-18x+2
frigid hollow
Nvm
agile roost
it's having different outputs for the same inputs that makes them analytically i...
I think this is what you mean
x^x is a function, it isn't multivalued either
frigid hollow
it's having different outputs for the same inputs that makes them analytically i...
Ohhh but how is this possible
frigid hollow
x^x is a function, it isn't multivalued either
But it doesn’t have an inverse
agile roost
that's the element of multivalued functions, they aren't actually functions
frigid hollow
cuz its not one to one
agile roost
yes, many to 1 functions don't have an inverse
agile roost
yes
frigid hollow
Oh so like abs(x) lmao
frigid hollow
Makes sense
agile roost
Oh so like abs(x) lmao
not really
frigid hollow
Ahhh lmao the same thing as one to many
frigid hollow
not really
Nvm
I should have said +-x is a multivalued function
But cya
Confused one to many with many to one AGAIN 💀
Oh man i love functions
agile roost
I just made it up
frigid hollow
makes sense tho i like it
agile roost
thank you
frigid hollow
I was gonna say “arc is misleading cuz its not a trig function”
But
Complex numberline and real number line use the unit circle for polar coordinate representation so
agile roost
it's a theoretical thing, just forms a circle in C for outputs
frigid hollow
It does indeed make perfect sense
agile roost
cya
frosty mulch
could anyone help me solve this?
dusty swallow
<@468053685805514752> “your” channel is being tainted rn
Thx for the notice btw
If ur part of the community for long enough
I might allow u back into riddles chat lmao
(I have no power)
frigid hollow
T ≈ 503.370175
where $\frac{52.5}{e^{\left(6.95805-\frac{1346.773}{x+219.693}\right)}}+\frac{97.5}{e^{\left(7.06623-\frac{1507.434}{x+214.985}\right)}}=1$
vivid gulchBOT
RamDejin
frigid hollow
x is T here
hollow ice
there is no inverse operation to modulus
Mwuahahahaha there is if we make the operation rather useless. There exists a distinct set $k$ such that $k=|k|$. If we restrict operation to $k \in \bR^+$ it has the invertibility property
vivid gulchBOT
cute little kitty
frigid hollow
Mwuahahahaha there is if we make the operation rather useless. There exists a di...
Modulus isn’t absolute value as he described eariler
hollow ice
Modulus isn’t absolute value as he described eariler
Modulus is well-defined as abs value in complexes
frigid hollow
If the distinct set k is such that k belongs to R+ then its just abs(k)
hollow ice
It might be different for other sets
frigid hollow
Because abs() takes real inputs
hollow ice
But for complexes it’s just $\sqrt{\Re(z)^2 + \Im(z)^2}$
vivid gulchBOT
cute little kitty
frigid hollow
but for your set its just abs(k)
Which we described has an inverse operation (plus minus k)
hollow ice
but for your set its just abs(k)
You denote modulus of complex k as $|k|$
vivid gulchBOT
cute little kitty
vivid gulchBOT
cute little kitty
frigid hollow
You also denote absolute value of a real value x as $|k|$
hollow ice
Yes?
vivid gulchBOT
RamDejin
hollow ice
The operation is identical for real values
So I don’t see the concern
$\bR \subset \bC$
vivid gulchBOT
cute little kitty
hollow ice
$|z|$ is well-defined over $\bC$, so it is also well-defined over $\bR$
vivid gulchBOT
cute little kitty
frigid hollow
So again, the inverse for your set was already defined for Real numbers as it is plusminus x, but you can’t do the same for modulus
It’s not the same inverse
hollow ice
So again, the inverse for your set was already defined for Real numbers as it is...
What is different about modulus over $\bR^+$?
vivid gulchBOT
cute little kitty
hollow ice
And modulus(z) is sqrt(z*z)
Yes
frigid hollow
But it isnt the same for real numbers
frigid hollow
nvm
hollow ice
$\sqrt{\Re(z)^2} = |z|$
vivid gulchBOT
cute little kitty
hollow ice
Since $\Im(z) = 0$
vivid gulchBOT
cute little kitty
hollow ice
As $z$ is real
vivid gulchBOT
cute little kitty
hollow ice
$\sqrt{z^2} = \Re(z)$ if z is real
vivid gulchBOT
cute little kitty
hollow ice
If it is non-real, not so much
frigid hollow
so it is different…
hollow ice
so it is different…
It is, but not in this context
frigid hollow
Okay
hollow ice
I said we can find inverse over $\bR^+$
vivid gulchBOT
cute little kitty
hollow ice
As $\bR^+ \subset \bC$, we can use modulus definition
vivid gulchBOT
cute little kitty
hollow ice
The modulus is defined as $\sqrt{\Im(z)^2 + \Re(z)^2}$, no?
vivid gulchBOT
cute little kitty
hollow ice
As our value is real, we have $\Im(z) = 0$
vivid gulchBOT
cute little kitty
frigid hollow
never seen that definition highkey
hollow ice
And also that $\Re(z) = z$
vivid gulchBOT
cute little kitty
hollow ice
never seen that definition highkey
It’s identical to $\sqrt{z \bar{z}}$
vivid gulchBOT
cute little kitty
frigid hollow
that's what im saying
i didnt know z*z = (Im(z))^2+(Re(z))^2
ohhh
i get it now
hollow ice
z*bar(z) = Re^2 + Im^2
hollow ice
Conj(z) = z if z is real
frigid hollow
i thought it could be complex too for some reason
hollow ice
Nah
frigid hollow
i am new to Im() and Re() functions
first time is saw it is when i was trying to simplify cos(x^2)
result was Re(e^(ix^2))
which made sense
but i never looked into the applications of Im()
ohhhhhhh lmao
sin(x^2) would be ${Im(e^(ix^2))}/i$?
i cant Latex
agile roost
Mwuahahahaha there is if we make the operation rather useless. There exists a di...
"if we.... then we... so then..." shut the fuck up
hollow ice
lmao
agile roost
sin(x^2) would be ${Im(e^(ix^2))}/i$?
yes, this is often used in CA
namely contour integrals which is a fun one
or integration by complex substitution
agile roost
complex analysis
agile roost
yeah, Gauss' signature is cool
frigid hollow
Yeah bro got an integral AND PI in his signature he really was a math geek
Like there’s no way the pi and the integral is a coincidence right?
Lol then again i’d have to ask gauss to know for sure
frigid hollow
Wrote this yesterday and realized why it’s wrong to assume integral of f(x) is the product dy*dx
Because if you set dy and dx as constant functions but then you find the reciprocal dx/dy, it should give the derivative of the inverse function of f(x) =x^2 automatically
But it doesn’t you have to make the switch from x to the inverse function f^(-1)(x) into the dx and dy equations for it to be valid and make sense by finding the derivative of the inverse
frigid hollow
Wrote this yesterday and realized why it’s wrong to assume integral of f(x) is t...
If the integral of f(x) really was the product dx and dy, then we shouldnt have to put y inverse in the derivative calculations, we could just put x and expect to get the derivative of the inverse
this helped clear it all up lol
normal arrow
wrong
it is more correct to say
$\frac{d}{dx}[f^{-1}(x)] = \frac{1}{f'(f^{-1}(x))}$
vivid gulchBOT
John Math
frigid hollow
**John Math**
its not the same x both sides
😂
oh lol it should mean the samething
no
yes nvm lol
yea just x is the general correct formula
mb
im still confused on why they have a different subscript for X in the equation
cuz u generally just write F^-1(x)
frigid hollow
$^{\infty}\left(x\right)=x+1$ i need help finding what value of x this converges to
vivid gulchBOT
RamDejin
frigid hollow
for x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x^{x}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} = x+1
the answer is about 1.4416...
but we know this converges since we can observe that x has to be greater than 1
idk how tho
thanks to anyone who can help!
frigid hollow
@burnt nest
using a graphing calculator might save you from future brain fog/death moments
burnt nest
yeah there is no root
wild pendant
It's a line touching the x axis
wild pendant
Therefore it is a root
frigid hollow
the root of the equation
wild pendant
Right?
frigid hollow
its what makes the y 0
loud lakeBOT
@frigid hollow has given 1 rep to @wild pendant
burnt nest
√4 is 2.7183 ?
wild pendant
Think of it as a function
frigid hollow
thank you for putting in that effort to use brain power
wild pendant
Where f(x) = 0
frigid hollow
√4 is 2.7183 ?
oh my god
burnt nest
f ( x ) = √4
frigid hollow
do you know what root means jado?
wild pendant
What
burnt nest
square root
wild pendant
√4 = 2
frigid hollow
f ( x ) = √4
thats not a function 💀
burnt nest
it is
burnt nest
f(x) = 2x is a function
frigid hollow
yes
wild pendant
f(x) = 2x is a function
It's a line going from 0,0
frigid hollow
does that look like f(x) = 2x to you?
burnt nest
f(x) = √4 is also one
wild pendant
What
wild pendant
Now I'm brainded too XD
burnt nest
Yeah
frigid hollow
ok
wild pendant
Thank god I have algebra lesson tomorrow
burnt nest
I already did
burnt nest
yes i did
wild pendant
Functions are graphs pretty much where for same Ys you must have different Xs
frigid hollow
then how can you say f(x) = sqrt(4) is a function
burnt nest
f(x) = 2x
so if x axis is a number means x axis is a √4
and if y axis is a number means y = √16
frigid hollow
f(x) = 2x
so if x axis is a number means x axis is a √4
and if y axis is a num...
x axis cannot be a number
its an axis
wild pendant
The x axis always has Y=0
frigid hollow
aka when y=0
frigid hollow
The x axis always has Y=0
this
wild pendant
And Y axis always has x = 0
frigid hollow
also true
wild pendant
That's all it does I think
burnt nest
aka when y=0
if y = root 16 means x = √x
frigid hollow
It's the other way around XD
even the other way around it isn't true
wdym for same x's it has different y's?
thats not a function either
wild pendant
I mean
burnt nest
Oh wait i understand now
frigid hollow
a function (or a one to one function which is usually what we learn about first) has a unique y value for every unique x value
burnt nest
if a value is in the x asis and y = 0 means x = √a
frigid hollow
💀
no bro
you're confusing roots of a function with the operator square root @burnt nest
wild pendant
That's what I'm trying to say
frigid hollow
and?
yeah but u didn't define what a function actually was
and its neither of the 2 definitions you provided
for instance
f(x) = x^x is not an injective function because you get the same y value at x=0.5 and x=0.25
frigid hollow
The x axis can also be a positive value
sure, so can the y axis
burnt nest
√4 is irrational
frigid hollow
no 💀
wild pendant
√4 = 2
frigid hollow
2 is not irrational
wild pendant
Because 2^2 = 4
frigid hollow
its quite the opposite of irrational
burnt nest
irrational is a number that ends ,0
frigid hollow
its like the most rational number in the history of existence after 1
burnt nest
ok
wild pendant
Irrational number is a number that always goes on and on pretty much
frigid hollow
is √2 rationak
no thats irrational
burnt nest
but there is clearly 2
frigid hollow
Irrational number is a number that always goes on and on pretty much
and never repeats the same pattern
the actual definition of irrational is
frigid hollow
a number that cannot be expressed in terms of $p/q$ where p and q are integers
vivid gulchBOT
RamDejin
burnt nest
so √3 is irrational
frigid hollow
yes!
wild pendant
Yes
vivid gulchBOT
wild pendant
So is √5
burnt nest
and √16 ?
wild pendant
No
frigid hollow
no
wild pendant
4^2 = 16
frigid hollow
,w sqrt(16)
vivid gulchBOT
frigid hollow
see how it ends at 4?
frigid hollow
see how this does not end?
burnt nest
,w sqrt(99990999999)
vivid gulchBOT
frigid hollow
irrational
wild pendant
That's an irrational number
burnt nest
wow
frigid hollow
do a smaller number, test all the numbers between 1 to 10 and tell us if u think its rational or irrational @burnt nest
your hw for tn
burnt nest
i thought that √99990999999 is 33330333333
frigid hollow
no
frigid hollow
square roots don't work like that
burnt nest
,sqrt (1)
burnt nest
,w sqrt(1)
frigid hollow
,
vivid gulchBOT
burnt nest
rational
burnt nest
,w sqrt(2)
vivid gulchBOT
frigid hollow
?
burnt nest
thats a big number
frigid hollow
no
burnt nest
means irrational
frigid hollow
there is a decimal point
burnt nest
oh
frigid hollow
its a bit below 1.5 but the number of digits after the point is alot
frigid hollow
and do u see the comma
frigid hollow
means irrational
it is irrational btw
burnt nest
yeah
frigid hollow
but its not a big number
burnt nest
at the beginning
frigid hollow
i mean do u see the three dots . . . after the digits?
burnt nest
yeah
frigid hollow
right below the number
burnt nest
yeah
frigid hollow
yeah that means there are more digits
an infinite amount of digits for all we know
burnt nest
it doesnt end
wild pendant
It goes on and on
burnt nest
ok
frigid hollow
but the value of the number is approximately about 1.414 right? and its a number below 1.5 so its not a big number but still irrational
burnt nest
so f ( x ) = √2 is irrational
burnt nest
but the **value of the number** is approximately about 1.414 right? and its a nu...
ah ok
frigid hollow
u number
wild pendant
F(x) means function
burnt nest
yeah
burnt nest
function is image
frigid hollow
tell us what u think
burnt nest
Wait
frigid hollow
function is image
KINDA! also called a group of relations
burnt nest
i found a way
frigid hollow
but u don't need to learn that
burnt nest
i just revise square roots
burnt nest
,w sqrt(3)
vivid gulchBOT
burnt nest
irrational
wild pendant
Yee
burnt nest
its 2 right
wild pendant
Mhm
burnt nest
,w sqrt(2)
vivid gulchBOT
frigid hollow
Test for 4 not 2 haha
wild pendant
?
burnt nest
,w sqrt(4)
vivid gulchBOT
frigid hollow
Yesss what do u think?
burnt nest
rational
wild pendant
Nice
burnt nest
in school i learned rational numbers are like 1/2
frigid hollow
Actually
burnt nest
4/3
wild pendant
No
frigid hollow
in school i learned rational numbers are like 1/2
Yessss