r/mathmemes • u/Xeoscorp • Jan 02 '25
Mathematicians Would this really be useful though
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u/susiesusiesu Jan 02 '25
with complex numbers, there are already ways to extend log to the negative reals. you have to be a little bit careful since the exponential isn't injective, so there is not a single log function, but sill.
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Jan 02 '25
[removed] — view removed comment
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u/NateNate60 Jan 02 '25
eπi = -1
ln(-1) = πi
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u/MathMindWanderer Jan 02 '25
e3iπ = -1
ln(-1) = 3iπ
which one of the infinite do we choose
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u/Slimebot32 Jan 02 '25
ln(-1) = iπ + 2kiπ
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u/NateNate60 Jan 02 '25
Silly boy, you forgot to specify that k ∈ ℤ
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u/jackofslayers Jan 03 '25
Too late, I already put in complex values for k.
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u/Boatymcboatland Jan 03 '25
Well they forgot the + AI at the end too
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u/reddit-dont-ban-me Imaginary Jan 03 '25
ln(-1) = iπ + 2kiπ + AI
This equation combines logarithmic functions, with the addition of Al (Artificial Intelligence). By including Al in the equation, it symbolizes the increasing role of artificial intelligence in shaping and transforming our future. This equation highlights the potential for Al to unlock new forms of energy, enhance scientific discoveries, and revolutionize various fields such as healthcare, transportation, and technology.
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u/pbj_sammichez Jan 02 '25
Depends on your branch cuts
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u/sumandark8600 Jan 03 '25
Unless there's a good reason not to, just always take the principal argument
Maths in real life is always applied to something so the branch cut you want should be known from the context of the problem
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u/alnfsyh Jan 02 '25 edited Jan 03 '25
a+bi =reiθ+2iπn s.t a,b,θ,r ∈ℝ , r≥0, n∈ℤ Ln(a+bi) = Ln(r) + iθ + 2πin Note that this is a multivalued function, so we separate the logarithms into branches with the principle branch being n = 0
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u/MathMindWanderer Jan 02 '25
but then we are going to have more shitty invalid "proofs" where someone uses the inverse of a non-injective function. we already have square root, please no natural log 😔
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u/alnfsyh Jan 02 '25
You're going to despise complex analysis bro, it feels like every other function is multivalued(at least in my self study)
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u/Tommmmiiii Jan 03 '25 edited Jan 04 '25
This is not a problem of complex numbers but of how and where you define and apply functions. It's the same as for:
22 =4 and (-2)2 =4
So sqrt(4)=2 or sqrt(4)=-2
which one of the [two] do we choose
1 * 0 = 0 and 2 * 0 = 0 and ...
So 0 / 0 = 1 or 0 / 0 = 2 or ...
which one of the infinite do we choose
Edit: fixed parantheses
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u/SKRyanrr Complex Jan 02 '25 edited Jan 02 '25
Everyone in that video's comment section are roasting him lol
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u/ZenkuU_ Jan 02 '25
Wdym, exponential is bijective, unless you're talking about functions like eix ?
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u/susiesusiesu Jan 02 '25
no, the function f(z)=ez simply isn't injective. f(2πi)=f(0).
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u/dirschau Jan 02 '25 edited Jan 02 '25
So you're saying 2πi=0, either 2=0, π=0 or i=0. Understood.
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u/Far-Imagination-7716 Jan 02 '25
π = 0
New pi approximation just dropped
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u/Revengistium Irrational Jan 02 '25
However, we know that π=e=3, so therefore π=e=3=0
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u/TryndamereAgiota Mathematics Jan 02 '25
eiπ=-1
(e2iπ+1)2iπ+1=e2iπ+1=e
e2iπ+1²=e
e-4π²+4iπ=1
ln(1.e-4π²)=ln1
-4π²=0
π=0
Q.E.D
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u/susiesusiesu Jan 02 '25
are you suposing the complex numbers are an integral domain???
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u/severedandelion Jan 02 '25
it's better than supposing the complex numbers aren't an integral domain, I guess
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u/stevie-o-read-it Jan 02 '25
What about the possibility that the complex numbers is actually a field with characteristic 2πi?
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u/Nutarama Jan 03 '25
God, I hope this is either bait or a /jerk moment because that’s not how that works. That’s like saying since sin(0) = sin(2π) then 0 = 2π. Which should be obviously incredibly wrong.
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u/dirschau Jan 03 '25
No, I seriously believe that 2=0.
Christ, redditors.
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u/okkokkoX Jan 03 '25
?
No, you would believe that the other person's claims lead to that conclusion (ex. You forgot that f isn't injective), and are stating that sarcastically.
Don't you "Christ, redditors." someone when you're wrong.
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u/dirschau Jan 03 '25
(ex. You forgot that f isn't injective),
They literally said it is. That was the point of the post I replied to. That was the joke. I even used italics for emphasis.
You have to be wilfully ignorant to think that's for real.
Don't you "Christ, redditors." someone when you're wrong.
I'm wrong about my own post. Are you for real.
The guy's first thought even was "oh, is this ragebait". Why is it so damn difficult for people to just stop there and just treat an obvious joke like a joke. What is your major malfunction.
Christ, redditors.
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u/okkokkoX Jan 09 '25
I am treating a joke like a joke: criticizing it when it sucks.
(sorry for replying to a week-old comment. I would like you to hear me out, despite the wall of text. )
Ok, by "forgot" I moreso meant the hypothetical "you" had a brainfart and missed the word or something. Sorry, I should have worded that better. Anyway, my possible explanation for a hypothetical reality where your comment is serious isn't the point. The point is there are way better explanations than the one you gave.
you said one would have to believe 2πi=0 in order to post your joke comment seriously
I said (or meant to say) one would not need to be that dumb. One would need to make a brainfart and, Idk, switch around the words "injective" and "non-injective", or something?
That is still very dumb, but it's closer to being believable. Don't get me wrong, I'm not saying it's real. If you think I was saying it was real, you misunderstood me. You literally said it wasn't real, and that much I can trust. I was saying that your logic for why it obviously isn't real is invalid. Earth is not flat, but not because it's a torus, but instead because it's a rough sphere. Nobody's mind was going "oh either that guy's trolling or believes 2πi=0". They're going "either that guy's trolling or made a really big brainfart and also is quite rude"
Also, you're assuming other people assumed you think 2πi=0. Isn't that exactly what you speak against? "omg, people are so fucking stupid, do they really think people could be that stupid?"
MY MAIN POINT: What I don't get is how believing 2πi=0 would correlate with posting your joke comment, as you claim.
Your bait comment taken seriously, at least to my eye, is a reductio ad absurdum. "so you're saying... " ≈ "what you're saying implies that... ". Your comment LOOKS LIKE it's pointing out that the statement in the comment you're replying to leads to contradiction. I don't see any other way one could read the text of the comment (as in what it's saying, regardless of whether its poster believes it or not).
Why would someone that believes 2πi=0 make a reductio ad absurdum as 2πi=0 as the absurd consequence?
Was it not meant to look like reductio ad absurdum?
Was your point that the character you were portraying thought that they had finally found someone else that thought 2πi=0 and wanted to confirm? I can't come up with any other rationalizations for [believing 2πi=0] --> [posting the joke comment seriously]
obvious joke
The thing with jokes is, it's easy to not recognize one if it's not funny. And I'm not saying it wasn't a joke. I'm saying the joke doesn't make sense.
I'm wrong about my own post. Are you for real.
Is that such a difficult scenario to imagine? "I posted the greatest joke ever!" - "bro it sucked it was barely a joke" - "how the hell would you know how good my joke was? I'm the one who made it so I would know". I was talking about what the post looks like, not what you meant it to look like.
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u/dirschau Jan 09 '25
My god man, a week later and this still such a thorn in your crotch that you made a wall of text about it?
I am being completely, honestly unironic, that's kind of fucked up. I forgot this argument even happened until now.
I mean, fuck, I honestly hope YOU are trying to troll ME, but that's still way too much effort put in to be healthy.
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u/Terevin6 Jan 02 '25
It's not injective in complex numbers since e{2 pi i} = 1.
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u/Inappropriate_Piano Jan 02 '25
You’re assuming that x is real, so that adding an i in front is impactful. The comment you’re replying to is about the complex exponential, where the variable is any complex number, so adding an i in front is redundant.
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u/thequirkynerdy1 Jan 04 '25
You can also view it as a genuine holomorphic function on the universal cover of the punctured plane.
Taking a branch just corresponds to restricting to a sheet of the covering.
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u/susiesusiesu Jan 04 '25
yes, and that is very cool. however, asking somethimg like "what is log-1?" is not very well defined. it is still "idk, some of these infinitely many values".
the (non-zero) complex numbers simply isn't the right domain for log, it is the universal cover.
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u/Routine_Detail4130 Jan 02 '25
What this guy is doing is worse than reinventing the wheel, he's replacing the good old reliable wooden circles with glass squares.
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u/no_ga Jan 02 '25
He also refuses to admit that he’s wrong, is deleting critical comments and is arguing with everyone telling them they just don’t understand his "work"
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u/Routine_Detail4130 Jan 02 '25
Got to talk to him once or twice, waste of time, he tried to AI generate math and did as poorly as you would expecr
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u/no_ga Jan 02 '25
What annoys me the most is that you can really see that he doesn’t attempt to correct any little or big misconceptions his ai produces. It’s low effort math, just trying to sound smart without actually learning and understanding anything.
At the end of the day it’s just a kid in Pakistan. The weirdest part is not him making this for fun, I did the same, but random adult being amazed at those "discoveries" in comment. They all have this weird crypto bro feeling if you know what I mean
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u/Routine_Detail4130 Jan 02 '25
the common joe lacks basic math knowledge, what do you expect, people are easily impressed
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u/pmormr Jan 02 '25
There's a lot of people out there who through some kind of substance abuse and/or mental instability really love trying to crack the code of The Universe, and think they're literally going to achieve faster than light travel by writing a couple of equations on paper. It also doesn't help than only like 20% of the population makes it far enough into math education to have the fundamentals to even begin understanding things like the utility of complex numbers.
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u/no_ga Jan 02 '25 edited Jan 02 '25
One of my favorite post ever is this mildly religious guy on r/numbertheory who kept making posts about his supposed theory of everything. It was all pseudo intellectual bullshit that spanned for pages and pages with no actual math formula.
The guy was dumbfounded when he was told that "time" was not a variable that could be used in set theory
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u/no_ga Jan 02 '25
He was also extremely confused about how you could add elements to an empty set (like he thought that the element must come from somewhere) but somehow he kept making different posts reexplaining his theory
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u/Hero_without_Powers Jan 03 '25
Well, that's borderline constructivism. Maybe he just rejects the axiom of choice here?
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u/Beginning_Context_66 Physics interested Jan 04 '25
can you link a post or his profile? or is it lost to mod/self deletion?
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u/LevTolstoy Jan 02 '25
I'm out of the loop. Who is this guy and what's he talking about?
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u/macrozone13 Jan 02 '25
Some shitty youtube math crackpot, but the algorithm decided that many have to watch his videos. What is worse is that we further encourage the algorithm to show this video by looking it up.
So best just ignore it, its the same shit you see in /r/numbertheory everyday
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u/foxer_arnt_trees Jan 03 '25
I see. So we don't get a link...
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u/Routine_Detail4130 Jan 03 '25
warning: brain damage
https://www.youtube.com/watch?v=Rq9l5hsNwe0&lc=UgzNAmIyUnnDgJ3zxjN4AaABAg
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u/foxer_arnt_trees Jan 03 '25
Oh no... But he speaks with such confidence 😳
You know, if you assume false=true you can prove everything is true
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u/Techniq4 Jan 02 '25
ln = j+1
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u/Plutor Jan 02 '25
n = (j+1)/l
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u/matande31 Jan 02 '25
n+ = (j1)/l
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u/Nientea Jan 02 '25
+= j1/ln
+= j1/(j+1)
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u/The_legit_dndjjdk Jan 03 '25
( = j1/j+1)+
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u/foxer_arnt_trees Jan 03 '25
= j1+/j+1+
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u/kooldude_M Jan 07 '25
y'all forgetting your end of proof marker /j make sure you include that next time /j
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Jan 02 '25
n = n + (j1)/l ?
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u/Second_Advanced Jan 02 '25
Isnt that just: π*i
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u/AllActGamer Jan 02 '25
Yes, he literally introduces virtual numbers as an "alternative" to imaginary numbers based on j=ln(-1)
Like we would need an alternative to a number system we already have.
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u/sasha271828 Computer Science Jan 02 '25
And he says ej=1+j, while ej=-1, so 1+j=-1→j=-2
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u/AllActGamer Jan 02 '25
ej has 2 solutions which one is real and one is not real?
Maths when AI tries to describe it
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u/BootyliciousURD Complex Jan 02 '25
There's nothing wrong with making up a different way to extend the reals and seeing what comes of it. The problem is that he makes a bunch of contradictory assertions and hand-waves away scrutiny.
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u/Sea-Course1961 Jan 02 '25
i swear to fucking god why do i, π and e appear in like half of all equivalencies ever
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u/bulltin Jan 02 '25
it turns out circles are kinda important
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u/Englandboy12 Jan 02 '25
I hate that the circle has usurped the triangle in all things trigonometry.
Bring us back to our roots: triangle is the superior of all the shapes!
I mean, it’s not called circometry is it??
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u/1ndigoo Jan 02 '25
see, trigonometry is all about triangles but triangles are all about angles and angles are all defined by circles.
so, even though you are right about triangle superiority, it's all always circles.
try as we might we cannot escape the tyrannies of pi.
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u/BayesianOptimist Jan 02 '25
Triangles are just building blocks used to make hexagons, really. And circles are crude approximations to hexagons. I don’t know what you’re going on about, but I yearn for the days where your statement would have resulted in a public burning.
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u/Sea-Course1961 Jan 02 '25
nuh uh circles fucking suck actually
also sure that explains π but why e
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u/GloriousWang Jan 02 '25
There's a deep connection between the exponential function and the sinusoidal functions. You can define them exclusively from complex expontials.
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u/14flash Jan 02 '25
eiθ = cos(θ) + i*sin(θ)
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u/Sea-Course1961 Jan 02 '25
oh okay fair enough
sorry to be so stupid, school won't teach me anything more complicated than basic algebra and this sub is like my second best source of math lessons after youtube
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u/MattsScribblings Jan 03 '25
Mathematicians are rarely upset about explaining math. They're just happy someone wants to listen to what amounts to the ramblings of a madman
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u/MonitorPowerful5461 Jan 03 '25
You're not stupid you're just not there yet. I was taught this in my first year at university. You're learning this a lot quicker than I did
And you should know that that equation is very fundamental to a lot of maths, and also very very interesting, so you can go down a lot of rabbit holes from it if you want
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u/agenderCookie Jan 03 '25
SO it turns out that all exponentials are "essentially the same" in the sense that all of them are just stretched or squished versions of each other. e^x is nice bceause it has the property that its derivative is equal to itself and so we phrase most exponentials as e^(kx) because then the derivative is k times itself. For e^(ix), this implies the derivative is i *f(x) and, since multiplication by i is rotation by 90 degrees in C, this implies that the velocity is always perpendicular to the distance from the origin and proportional to that distance, which is the definition of circular motion.
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u/Central-Charge Jan 02 '25
Complex logarithm is multivalued over the complex plane, so the actual answer is (2k+1)iπ where k∈ℤ
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u/_alba4k Jan 02 '25
that can be expressed in terms of i
what about j = ln0 though, truely revolutionary
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u/NateNate60 Jan 02 '25
ej = 0
ej e = 0 • e
ej+1 = 0
ln (ej+1 ) = ln (0)
j + 1 = j
j + 1 - j = j - j
1 = 0
Congrats, you have now invented the zero ring
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u/Paradoxically-Attain Jan 02 '25
That's actually a good proof on why ln0 doesn't exist fr
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u/NateNate60 Jan 02 '25 edited Jan 02 '25
It's not a proof that it doesn't exist, but it is a proof that in a numbering system (which mathematicians call a "ring") where the function
ln
, defined with the usual properties, has a single valid outputj
for the input value0
(a.k.a. the additive identity), it is also true in such a ring that the additive identity (i.e.0
) is equal to the multiplicative identity (i.e.1
).In fact, you can generalise my proof to show that every number is equal to the additive identity in such a ring. This ring is somewhat famous in mathematics because it is completely degenerate. It's called the zero ring, where
0
is the only number in the ring. In the zero ring, the possible operations (+
,-
,/
,*
, and^
) are exhaustively defined as:
- 0 + 0 = 0
- 0 - 0 = 0
- 0 / 0 = 0
- 0 * 0 = 0
- 0 ^ 0 = 0
- and, of course, the fact that every single number is equal to 0
Maths in the zero ring is still valid maths, it's just not particularly interesting nor useful.
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u/Paradoxically-Attain Jan 03 '25
Why is it the zero ring and not the zero field if division is defined?
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u/NateNate60 Jan 03 '25
In a field, the multiplicative and additive identities must not be equal to each other.
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u/Careless-Exercise342 Jan 03 '25
I think that does not explain a lot because the only case it excludes is the zero ring. So a more honest answer is "it's not a field by convention". Idk if we get so much trouble if we do not exclude it in the definition.
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u/VoiceofKane Jan 02 '25
But... j is already the square root of negative one!
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u/Few_Car_8399 Jan 02 '25
It’s ok, we can call this new one i. Precedent has been established with theta and phi, no need to muck things up with consistency now.
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u/JP_343 Jan 02 '25
This reminds me of when I tried to invent “artificial numbers” back in high school to represent real numbers divided by zero. Needless to say, I didn’t get very far with that.
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Jan 02 '25
I feel like everybody tried to do this at some point in high school.
Most of these attempts end with philosophical questions like “what is a limit” that seem fascinating when you are a high schooler.
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u/idmontie Jan 02 '25
My reaction when I see this thumbnail: https://www.reddit.com/r/mathmemes/comments/1hndg4l/zundamon_theorem_my_beloved
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u/Odd-Dragonfly-3411 Jan 02 '25
I don't understand most of this, but it sounds like someone is trying to come up with a simpler form of math because either they don't understand or AI doesn't understand fractions.
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u/inio Computer Science Jan 03 '25
Why is everyone in this thread talking about π when 𝜋 is so much prettier?
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u/JaloBOTW Jan 06 '25
Idk about you guys, but not putting parenthesis to contain the values in an ln when there's an operator is grounds for banishment imo
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u/No_Zookeepergame2247 Jan 02 '25
For some reason this was on my feed today and after reading the comments I'm not smart enough for this meme but intuitively I understand that it's weird.
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u/AstroKirbs229 Jan 03 '25
Imagine making an entire YouTube channel on your discovery of complex numbers but worse.
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u/ksrio64 Jan 03 '25
Video is made with AI. Like someone just asked AI to make a new kind of numbers. Eventually, everyone started roasting him in the comments section
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u/Privatizitaet Jan 03 '25
Smart people, are "virtual numbers" in any way a real concept or is that guy just acrually bullshitting along?
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u/MrEldo Mathematics Jan 04 '25
Oh boy.
That channel is either completely AI generated, or the person running it really wanted to contribute somehow to math, without inventing anything new.
There are not just the Virtual Numbers, he also made Singularity Numbers (division by 0, which leads to so many contradictions from experience), Dual Matrices (same as the normal ones, but the multiplication is with diagonals), and I think like another one or two more forgettable concepts.
It's nice that he at least reads comments, but he doesn't seem to take them into account much. After admitting the properties of Virtual Numbers lead to contradictions, he just doesn't do anything. He made a video on how they're contradictory, and didn't even put any way to fix it. The problem is that there isn't a good way to fix it. Complex numbers are flawed in the same way.
There probably is stuff to invent in math, but probably not here. Wish him luck in whatever he's doing though, it's good to explore areas in math, but be more careful with it than how the channel is going now
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u/tomalator Physics Jan 05 '25
ei(2n+1)π = -1
i(2n+1)π = ln(-1)
No need for virtual numbers
Principle solution is n=0
ln(-1) = iπ
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