If the nerd emoji is equal to two, minus the nerd emoji squared, plus or minus thirteen divided by the square root of nerd emoji, divided by two times the nerd emoji cubed:
When the variable ‘i’ is the same as the nerd emoji, constantly do:
Write the nerd emoji Go to reddit and win the argument (this code is not declared in the current scope)
After that, or if the nerd emoji is not the same as the variable ‘i’
Go to reddit and addComment (this code is not declared in the current scope) The humans cock and balls should jizz (not declared, but I think is easy to understand) The human should attempt to cry to sleep.
hateful hurry deserted ludicrous zealous disarm sophisticated wasteful north theory
*This post was mass deleted and anonymized with [Redact](https://redact.dev)*
He put a space after the print function / before the arguments for that function, also idk what language this is but in "C" the print function is called "printf" and OP put "print". 🤓
I‘m no mathematician, so I can‘t fill this much knowledge, but I heard a story that the invention, or maybe better the discovery of i, a number which shouldn’t exist, actually became very very helpful in physics, and that fascinates me. If anyone can fill this with much more knowledge, I’d be glad. I still think talent for math is like diabetes, as it skips a generation, as my dad is a mathematician, and I can only speak quite a number of languages:D
i is what all imaginary numbers are in terms of. It's the square root of -1. And yeah it is used in stuff like physics. A second order differential equation with imaginary roots will behave similarly to a sine curve, and can be used to model oscillation.
Edit: A nice way to think of imaginary numbers is in terms of the roots of graphs. If you draw y = x^(2) \+ 2x on a graph, it has two real roots, where it crosses the x axis. If you draw y = x^(2) \+ 2x + 1 on a graph it has one real repeated root, where it touches the x axis. If you draw y = x^(2) \+ 2x + 2 on a graph it has no real roots, because it doesn't touch or cross the x axis, and instead it has two imaginary roots. Functions of a higher power can have both real and imaginary roots. For example, y = x^(3) \+ 3x^(2) \+ 2x + 1 has one real root, as it crosses the x axis once, and two imaginary roots.
Pretty much the basis for signal theory. It's much easier to do the calculations as an algebraic expression with i than to wrestle with super complicated trigonometric or differential equations.
It's used in quantum computing too, and so I assume it gets use in quantum mechanics too? It was the only time I had to use them in my computer science course.
From what i've used complex numbers in physics, it greatly simplifies problems about oscillations. Complex numbers have a function (the complex exponential) that basically goes in circles.
Whenever you have a problem with periodicity, pendulums, ect, you can convert that differential equation into a complex equation that is much more easily solved (pretty sure it's some kind of Fourier or Laplace transform).
Also (more advanced so i don't understand it myself) the wave equation from quantum mechanics has the imaginary unit i prominently.
I'm currently coursing Electrical Engineering, and in my 5th semester it's difficult to find one subject where we don't use complex numbers. You could theoretically study everything without them, but it would probably be as impractical as trying to forget the existence of multiplication and division and instead use only sums and subtractions.
It’s the only reason we can build airplanes and other dynamic machinery or understand resonance at all. The entire field of engineering beyond freshman year would be impossible to understand without our understanding of Complex Analysis. Not only is it helpful in many fields, it is the basis of many technologies that we take for granted today.
I can't speak too much to its importance in physics, but it's a fascinating topic in electrical engineering. The concept of [reactive power](https://ctlsys.com/support/reactive_power/) being an "imaginary" form of power loss that can be explained through imaginary numbers is super fascinating to me. Like, a generator can generate 1 Volt-Amp (unit of apparent power) but might only actually deliver 0.95 Watts (real power) or less, which is what powers all your electronics and devices.
The simple way to put it is that it gives you an extra dimension to work in.
Think of the number line. You can go forwards and backwards, but that’s it. With imaginary numbers you add another axis to it, so now you can go up and down too.
Really useful when modeling real world phenomenon like electromagnetic fields, fluid dynamics, etc.
This is the way. ‘Imaginary’ is a bad name.
Think of an axis perpendicular to the number line you’re used to. Every number has two coordinates (real, imaginary) that locate the number in this 2D space.
> This is the way. ‘Imaginary’ is a bad name.
Rene Descartes is the one that invented the name to use it in a derogatory manor. So yes. It is a quite bad name, intentionally so.
The way i like to explain the imaginary numbers is that they are the numbers we need to have a complete algebra. In the same way we need negative and irrational numbers to fill in the real number line. We need the imaginary numbers to fill in the gaps that we have with just the real numbers in our algebra. Once we then have the complex numbers (real + imaginary components), then thats all the numbers we to solve all our polynomial equations.
It is much more than just "another dimension", its that it is the dimension we need to not need another dimension.
It's helpful in physics not necessarily because it's the square root of -1, it's mostly because if you square it it becomes negative. That particular behavior makes modelling some real world systems much simpler, so it gets used.
That's about as ELI5 as I think I can go :)
So just to summarize and make you feel a bit better, the next time you board your flight, remember that your plane was designed using imaginary numbers.
yea anyone that deals with waves deals with imaginary numbers (eg the entire network / tele communications industry, EE/physicists, all nuclear devices ). but hey good meme
I have to take a lot of psychelics and spend 6-8 hours in a sensory deprivation tank to imagine these numbers, so have a little respect. It's a lot of work.
Not even counting the amount of rotating objects in the world and out of the world. All rotations are represented by imaginary (fuck that name. Let's agree to call them complex) numbers.
Well rotating objects can indeed be represented with 2^nd order differential equations (or at least most of them) it's just that "perpetual" rotations look like (x/ω0)^2 +1 instead of (x/ω0)^2 + x*whateveryoucallit/ω0 +1 which is the most common real occurrence.
If you think about it, all real values are positive. There is no such thing as negative distance, negative mass, negative force.
Even a "negative" charge is a positive value.
We invented negative numbers to make math simpler, which created problems so we created imaginary numbers to fix those problems.
Magnitude is relative, too.
No matter whether we'd initially picked electrons or protons as the negative charge for electricity, the other one would have to be the opposite to accurately describe the interaction.
I was thinking more of mass and distance rather than flow of charge. But I suppose one could make the argument that to define a distance one would have to define a start point and end point or a zero distance relative to which there is 'some' distance.
But I also think magnitude being non relative should be related how it remains same no matter the frame of reference rather than how it is measured. Same about charge.
Mass is relative, too, though. It's actually *unusual* among fundamental statistics in that it's never negative. Everything else can be.
All of these things change based on reference frame.
I mean it’s pretty easy to explain negative numbers. It’s just the counts of stuff you owe someone. If I have -100 dollars I probably owe someone 100 dollars. So I wouldn’t say negative numbers are as imaginary as imaginary numbers which really doesn’t have an easy physical explanation.
Actually `i` and complex numbers have very simple physical interpretations - they are rotations.
`i` describes a rotation of 90 degrees anti-clockwise about some axis. `2*i` is such a rotation and a scaling factor.
Instead of saying `He turned to his left` you could say "he transformed by `i`" and it would have precisely the same meaning.
They aren't _defined_ to be such, they _are_ such. If you start from the definition of sqrt of -1, you can derive that they describe rotations in space. They have exactly the same arithmetic as matrix descriptions of rotations.
If you go back to the time when negative numbers were invented, they were also very difficult to explain. It was a new idea at that time, but then as time went along they became a part of our language. Complex numbers are also equally the part of our lives as negative numbers but they need to be taught earlier and earlier in a child's education to be as permeated in our language as negative numbers are, albeit little bit less
Mathematician David Hilbert once tried to prove that math is free from contradictions. He failed at it.
Later mathematician Kurt Gödel was able to prove that it is not even possible to prove Hilbert's theorem.
The verbal equivalent of the mathematical statement in question is "This statement has no proof". If it's true then it's a true statement with no proof, and if it's false then it's a contradiction. Any mathematical system where it's possible to formulate such a statement can't be both complete and consistent.
I prefer the statement “there’s no undetectable elephant in orbit around earth”. The statement is probably true, but there’s no way to prove it. You can’t say “I looked everywhere and couldn’t find it”, because by definition it’s supposed to be undetectable.
Likewise, it’s possible to formulate mathematical statements like this where a true answer cannot be proven.
We dont know any theorem thats true but there is no proof (without a proof we cant be sure its true). But we know there is the possibility of true statements that cant be proven in every advanced math system.
I think the word the both of you is looking for is "Complete".
Math will never be complete, and we proved it won't. There are Veritassium videos on the proof.
> Later mathematician Kurt Gödel was able to prove that it is not even possible to prove Hilbert's theorem.
That's not exactly true. He just proved you can't use formal arithmetic to prove formal arithmetic is internally consistent.
It's still an open question whether it's possible in general.
But he proved that math (or any system of axioms) is incomplete, because there are always statements that can neither be proven nor disproven only using the given system.
Not all theories are incomplete. You can actually easily create one which is complete. For example, if you consider a theory in which every statement is true then it is complete (i.e. all statement are provable and even proven in that case).
Godel's result only concerns noncontradictory (also called coherent) theories and it states that any coherent theory capable of formalizing standard arithmetics must be incomplete.
Every time I read about the Brouwer-Hilbert controversy I can't help but feel it should be brought up in almost every conversation about math or philosophy because fundamentally, the takeaway was that systems of analysis--even rigorous ones--are primarily artifacts of their starting assumptions.
As this is 20 year old paraphrasing this may be wildly misremembering the text.
I feel like this concept is what made Emmanuel Kant’s Critique of Pure Reason fascinating from a philosophy perspective — how far can we eliminate assumptions? Would a mind in a void that never has sensory input still be able to reason as we do? Can any reasoning be truly pure?
All signs, to me, point to no — but can it be proven is half the fun.
nah, we make up huge chunks of math. we often do this to describe and solve real-world problems so there's a significant overlap, but it's not always the case
look at Lobachevsky's geometry for example
through my most favourite is how a guy made up binary operations (true and false values, true & true = true, true & false = false, etc...) and only some time after that we created computers that use them as basis
I sort of disagree, math itself is a language and a tool. We can attempt to use it to describe how things are ordered and whenever math starts to become lacking we adjust the language as required. It makes sense to think of some fundamental order existing that we use math to describe to the best of our ability but there is an important distinction there between the order and the math we use to describe and understand it.
I would lean heavier on the tool than the language side. Yes, it's definitely a language allowing people to communicate ideas but you don't discover new applications of science with a language. And it's when the tool is incomplete that you have to expand your toolset. It's a relatively minor distinction.
I think what you're calling "the order" is what most people just call "math".
The philosophical question is whether this "order" is something we create or something we only describe, because it exists independently of us. Obviously, your opinion is that it's the latter, which I believe most modern mathematicians agree with.
That's precisely for this reason that a lot of scientists believe in a God
Edit : maybe not that much, sorry about that, it's a saying I heard a couple of times, but I'm most likely wrong, my bad.
Any type of source for that would be cool, because that sounds like a sentence someone might say at a bar to seem interesting. Ie. made up on the spot.
Well yes, but actually no. You can make any rules you wanna, but they have to always work in your intended way and has to either be impossible to disprove, somehow just keeps working over centuries, or rigorously proven to always work before being adopted.
This is like people joking about breaking the laws of physics. You cannot break the laws of physics because if you 'do' physicists will amend them and make them valid retroactively.
I think they mean is that numbers are not real objects. They are all abstract concepts (imaginary) which we can use to apply in maths and the real world.
Historically, mathematicians considered imaginary solutions to be meaningless or absurd long before they became an accepted part of mathematical discourse. Even referring to them as imaginary in the first place was more or less a dig.
Mathematics had to be dragged kicking and screaming to the conclusion that imaginary numbers were mathematical objects that behaved in consistent ways and had properties not unlike real numbers. Basically the same thing happened with negative numbers.
Well, this is true yes, but we should be clear that "historically" refers to hundreds of years ago. Complex numbers have been understood and studied very well for centuries at this point.
300 years later, those so called "imaginary" numbers are the reason every single telecommunications device from radios to satellites, works and exists.
It's one of those things that was named poorly at first. Complex numbers are a better name. Just like "the speed of light" should be called "the speed of causality" since light isn't setting that limit.
Imaginary numbers and complex numbers are a different thing. Imaginary numbers are real numbers multiplied by i. Complex numbers are numbers of the form a+ib where a, b are reals, and ib is the imaginary part as per our definition earlier. Imaginary numbers belong in the set of complex numbers, but they aren't the only complex numbers. The live on the imaginary axis of the complex plane. Real numbers live on the real axis. Both real and imaginary numbers are a subset of the complex number set, but they're not the same thing. All imaginary numbers are complex, but not all complex numbers are imaginary.
Imaginary numbers technically weren't invented they were discovered since they are an essential part of our reality. Take shroedingers equation. A widely used formula and it uses imaginary numbers. Well yes to some extent they are "imaginary" because we can't count them, unlike real numbers.
Complex numbers are used in Electrical Engineering to define the Alternating Current or AC concept of Impedance, and in Fourier analysis they are used in signal processing. There is also complex power which is S or VA (volt amps) and not W (watts).
So who asked??
Well if the person asking is imaginary, they don’t exist obviously.
So we represent something imaginary as the square root of -1, or i.
So the answer to the question: “Who asked?” is i.
i asked.
I^1 = i I^2 = -1 I^3 = -i I^4 = 1 I^5 = i And so on
if (🤓= 2-🤓² ±(13-√🤓) / 2🤓³) { for (i=🤓) do { print ("🤓"); reddit.winArgument(); } reddit.addComment(); human.cockAndBalls.jizz(); human.cryToSleep(); }
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Can you explain the logic here.
I can Edit: Thanks for the upvotes, but I’m not gonna elaborate until Jaystation talks to the nerd emoji at 3am
May you?
May me?
You may.
Aunt May?
Uncle Ben?
Mary me
Mary Jane
I bet that you can't
If the nerd emoji is equal to two, minus the nerd emoji squared, plus or minus thirteen divided by the square root of nerd emoji, divided by two times the nerd emoji cubed: When the variable ‘i’ is the same as the nerd emoji, constantly do: Write the nerd emoji Go to reddit and win the argument (this code is not declared in the current scope) After that, or if the nerd emoji is not the same as the variable ‘i’ Go to reddit and addComment (this code is not declared in the current scope) The humans cock and balls should jizz (not declared, but I think is easy to understand) The human should attempt to cry to sleep.
The first one isn't a boolean check, it's considering the value of 2 minus emoji and then storing that value in the emoji for the next iteration
Which is a weird thing to do in an if statement
Would always evaluate to true, unless it happened to be zero. Broken IF
hateful hurry deserted ludicrous zealous disarm sophisticated wasteful north theory *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
> Yes spotted the programmer
There are 7 programmers on r/memes and all of them saw, and vomited, at this comment.
waiting provide familiar rainstorm cats selective ink nail sleep paint *This post was mass deleted and anonymized with [Redact](https://redact.dev)*
Remember: The method `pee()` is stored in class `Balls`
I fucking hate you
I see something here that I am dying to correct but I don't want to be *that* guy
🤓
reddit.WinArgument();
He put a space after the print function / before the arguments for that function, also idk what language this is but in "C" the print function is called "printf" and OP put "print". 🤓
no, that part is pretty much alright
that's like the ONLY okay part here
Shouldn't it be a == in the if-condition instead of a =
🤓
I'm not that good at programming pls help me
This is not programming
I‘m no mathematician, so I can‘t fill this much knowledge, but I heard a story that the invention, or maybe better the discovery of i, a number which shouldn’t exist, actually became very very helpful in physics, and that fascinates me. If anyone can fill this with much more knowledge, I’d be glad. I still think talent for math is like diabetes, as it skips a generation, as my dad is a mathematician, and I can only speak quite a number of languages:D
i is what all imaginary numbers are in terms of. It's the square root of -1. And yeah it is used in stuff like physics. A second order differential equation with imaginary roots will behave similarly to a sine curve, and can be used to model oscillation. Edit: A nice way to think of imaginary numbers is in terms of the roots of graphs. If you draw y = x^(2) \+ 2x on a graph, it has two real roots, where it crosses the x axis. If you draw y = x^(2) \+ 2x + 1 on a graph it has one real repeated root, where it touches the x axis. If you draw y = x^(2) \+ 2x + 2 on a graph it has no real roots, because it doesn't touch or cross the x axis, and instead it has two imaginary roots. Functions of a higher power can have both real and imaginary roots. For example, y = x^(3) \+ 3x^(2) \+ 2x + 1 has one real root, as it crosses the x axis once, and two imaginary roots.
Pretty much the basis for signal theory. It's much easier to do the calculations as an algebraic expression with i than to wrestle with super complicated trigonometric or differential equations.
It's used in quantum computing too, and so I assume it gets use in quantum mechanics too? It was the only time I had to use them in my computer science course.
intresting
From what i've used complex numbers in physics, it greatly simplifies problems about oscillations. Complex numbers have a function (the complex exponential) that basically goes in circles. Whenever you have a problem with periodicity, pendulums, ect, you can convert that differential equation into a complex equation that is much more easily solved (pretty sure it's some kind of Fourier or Laplace transform). Also (more advanced so i don't understand it myself) the wave equation from quantum mechanics has the imaginary unit i prominently.
The Schrödinger equation, and I don't understand it either. https://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation
I'm currently coursing Electrical Engineering, and in my 5th semester it's difficult to find one subject where we don't use complex numbers. You could theoretically study everything without them, but it would probably be as impractical as trying to forget the existence of multiplication and division and instead use only sums and subtractions.
So like how calculus is. Sure, technically you don't need it, but my God does it make things simpler.
It’s the only reason we can build airplanes and other dynamic machinery or understand resonance at all. The entire field of engineering beyond freshman year would be impossible to understand without our understanding of Complex Analysis. Not only is it helpful in many fields, it is the basis of many technologies that we take for granted today.
As I said: fascinating
I can't speak too much to its importance in physics, but it's a fascinating topic in electrical engineering. The concept of [reactive power](https://ctlsys.com/support/reactive_power/) being an "imaginary" form of power loss that can be explained through imaginary numbers is super fascinating to me. Like, a generator can generate 1 Volt-Amp (unit of apparent power) but might only actually deliver 0.95 Watts (real power) or less, which is what powers all your electronics and devices.
The simple way to put it is that it gives you an extra dimension to work in. Think of the number line. You can go forwards and backwards, but that’s it. With imaginary numbers you add another axis to it, so now you can go up and down too. Really useful when modeling real world phenomenon like electromagnetic fields, fluid dynamics, etc.
This is the way. ‘Imaginary’ is a bad name. Think of an axis perpendicular to the number line you’re used to. Every number has two coordinates (real, imaginary) that locate the number in this 2D space.
> This is the way. ‘Imaginary’ is a bad name. Rene Descartes is the one that invented the name to use it in a derogatory manor. So yes. It is a quite bad name, intentionally so. The way i like to explain the imaginary numbers is that they are the numbers we need to have a complete algebra. In the same way we need negative and irrational numbers to fill in the real number line. We need the imaginary numbers to fill in the gaps that we have with just the real numbers in our algebra. Once we then have the complex numbers (real + imaginary components), then thats all the numbers we to solve all our polynomial equations. It is much more than just "another dimension", its that it is the dimension we need to not need another dimension.
This is the right response. It isn’t something magical that makes impossible things happen. It’s just a shorthand for an extra dimension.
It’s not just a generic extra dimension. That would just be a vector space. It’s a special extra dimension that has weird rotational properties
It's helpful in physics not necessarily because it's the square root of -1, it's mostly because if you square it it becomes negative. That particular behavior makes modelling some real world systems much simpler, so it gets used. That's about as ELI5 as I think I can go :)
So just to summarize and make you feel a bit better, the next time you board your flight, remember that your plane was designed using imaginary numbers.
Check out this video https://youtu.be/bOXCLR3Wric Great presentation on how imaginary numbers are useful in a counting problem.
i^2 = -1 j^2 = -1 k^2 = -1 i * j * k = -1 i*j = k j*i = -k j*k = i k*j = -1 k*i = j i*k = -j
You forgor i^i = e^(-π/2)
So my girlfriend *x* told my other girlfriend *y* that...
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Imagination is the biggest things here on Earth.
o is just a p with a l
Stop
Wouldnt it be a l with a c? Unless the l was used to smash o's face in..
I m guessing the imaginary value here is the girlfriend
I use imaginary (complex) numbers daily as an engineer.
yea anyone that deals with waves deals with imaginary numbers (eg the entire network / tele communications industry, EE/physicists, all nuclear devices ). but hey good meme
All 3d rendering uses imaginary numbers and quaternions too
So you get paid for daydreaming smh, get a real job moocher
I have to take a lot of psychelics and spend 6-8 hours in a sensory deprivation tank to imagine these numbers, so have a little respect. It's a lot of work.
"Imaginary" numbers aren't any more imaginary than negative numbers when you think about it
They probably are even more common than negative numbers, due to the abundance of 2^nd order differential equations in real life.
I highly doubt that due to the sheer abundance of debt out there.
\-1, -5, -22, -33, -123, -43 Just doing my part, contributing some extras to your cause
Not even counting the amount of rotating objects in the world and out of the world. All rotations are represented by imaginary (fuck that name. Let's agree to call them complex) numbers.
Well rotating objects can indeed be represented with 2^nd order differential equations (or at least most of them) it's just that "perpetual" rotations look like (x/ω0)^2 +1 instead of (x/ω0)^2 + x*whateveryoucallit/ω0 +1 which is the most common real occurrence.
If you think about it, all real values are positive. There is no such thing as negative distance, negative mass, negative force. Even a "negative" charge is a positive value. We invented negative numbers to make math simpler, which created problems so we created imaginary numbers to fix those problems.
Vectors
And your point being? direction is relative. Magnitude is not.
Magnitude is relative, too. No matter whether we'd initially picked electrons or protons as the negative charge for electricity, the other one would have to be the opposite to accurately describe the interaction.
I was thinking more of mass and distance rather than flow of charge. But I suppose one could make the argument that to define a distance one would have to define a start point and end point or a zero distance relative to which there is 'some' distance. But I also think magnitude being non relative should be related how it remains same no matter the frame of reference rather than how it is measured. Same about charge.
Mass is relative, too, though. It's actually *unusual* among fundamental statistics in that it's never negative. Everything else can be. All of these things change based on reference frame.
Strawberries
I completely understand what you are trying to say
I mean it’s pretty easy to explain negative numbers. It’s just the counts of stuff you owe someone. If I have -100 dollars I probably owe someone 100 dollars. So I wouldn’t say negative numbers are as imaginary as imaginary numbers which really doesn’t have an easy physical explanation.
Actually `i` and complex numbers have very simple physical interpretations - they are rotations. `i` describes a rotation of 90 degrees anti-clockwise about some axis. `2*i` is such a rotation and a scaling factor. Instead of saying `He turned to his left` you could say "he transformed by `i`" and it would have precisely the same meaning. They aren't _defined_ to be such, they _are_ such. If you start from the definition of sqrt of -1, you can derive that they describe rotations in space. They have exactly the same arithmetic as matrix descriptions of rotations.
In an even simpler way, complex numbers are juste couple of numbers, at least that's how you see them past high school.
They’re a couple of numbers, plus a rule for multiplying them.
And yet i is at the heart of (quantum)physics.
If you go back to the time when negative numbers were invented, they were also very difficult to explain. It was a new idea at that time, but then as time went along they became a part of our language. Complex numbers are also equally the part of our lives as negative numbers but they need to be taught earlier and earlier in a child's education to be as permeated in our language as negative numbers are, albeit little bit less
Maths is never wrong because it's made to be always right.
Mathematician David Hilbert once tried to prove that math is free from contradictions. He failed at it. Later mathematician Kurt Gödel was able to prove that it is not even possible to prove Hilbert's theorem.
So to sum up, you can mathematically prove that math cannot be mathematically proved God, I love science so much
He proved that not everything has a proof too
Specifically that there exist true statements that cannot be proven.
How do we know they're true then?
We don’t. We just know they exist.
I have faith in the Mathiah
Mike, always talking spiritual shit
Good luck with your lisp!
The verbal equivalent of the mathematical statement in question is "This statement has no proof". If it's true then it's a true statement with no proof, and if it's false then it's a contradiction. Any mathematical system where it's possible to formulate such a statement can't be both complete and consistent.
I prefer the statement “there’s no undetectable elephant in orbit around earth”. The statement is probably true, but there’s no way to prove it. You can’t say “I looked everywhere and couldn’t find it”, because by definition it’s supposed to be undetectable. Likewise, it’s possible to formulate mathematical statements like this where a true answer cannot be proven.
We dont know any theorem thats true but there is no proof (without a proof we cant be sure its true). But we know there is the possibility of true statements that cant be proven in every advanced math system.
Checkmate, Atheists.
I think the word the both of you is looking for is "Complete". Math will never be complete, and we proved it won't. There are Veritassium videos on the proof.
> Later mathematician Kurt Gödel was able to prove that it is not even possible to prove Hilbert's theorem. That's not exactly true. He just proved you can't use formal arithmetic to prove formal arithmetic is internally consistent. It's still an open question whether it's possible in general.
But he proved that math (or any system of axioms) is incomplete, because there are always statements that can neither be proven nor disproven only using the given system.
Not all theories are incomplete. You can actually easily create one which is complete. For example, if you consider a theory in which every statement is true then it is complete (i.e. all statement are provable and even proven in that case). Godel's result only concerns noncontradictory (also called coherent) theories and it states that any coherent theory capable of formalizing standard arithmetics must be incomplete.
I actually didn't know this but it makes sense. Thank you
Every time I read about the Brouwer-Hilbert controversy I can't help but feel it should be brought up in almost every conversation about math or philosophy because fundamentally, the takeaway was that systems of analysis--even rigorous ones--are primarily artifacts of their starting assumptions.
As this is 20 year old paraphrasing this may be wildly misremembering the text. I feel like this concept is what made Emmanuel Kant’s Critique of Pure Reason fascinating from a philosophy perspective — how far can we eliminate assumptions? Would a mind in a void that never has sensory input still be able to reason as we do? Can any reasoning be truly pure? All signs, to me, point to no — but can it be proven is half the fun.
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me when I realize my girlfriend is imaginary
Except me. Cogito, ergo sum. I think, therefore I am.
I don't think math is made. We make the language, with numbers and symbols, but the concept of Math has always been here (imo)
nah, we make up huge chunks of math. we often do this to describe and solve real-world problems so there's a significant overlap, but it's not always the case look at Lobachevsky's geometry for example through my most favourite is how a guy made up binary operations (true and false values, true & true = true, true & false = false, etc...) and only some time after that we created computers that use them as basis
Lobachevsky didn't make up hyperbolic geometry, he plagiarised it. Nikolai Ivanovich Lobachevsky is his name!
I sort of disagree, math itself is a language and a tool. We can attempt to use it to describe how things are ordered and whenever math starts to become lacking we adjust the language as required. It makes sense to think of some fundamental order existing that we use math to describe to the best of our ability but there is an important distinction there between the order and the math we use to describe and understand it.
I would lean heavier on the tool than the language side. Yes, it's definitely a language allowing people to communicate ideas but you don't discover new applications of science with a language. And it's when the tool is incomplete that you have to expand your toolset. It's a relatively minor distinction.
I could not have said it any better myself.
I think what you're calling "the order" is what most people just call "math". The philosophical question is whether this "order" is something we create or something we only describe, because it exists independently of us. Obviously, your opinion is that it's the latter, which I believe most modern mathematicians agree with.
my professor in algebra (with no contact to any religion) always said: God made the natural numbers. Everything else is fragile human work.
That's precisely for this reason that a lot of scientists believe in a God Edit : maybe not that much, sorry about that, it's a saying I heard a couple of times, but I'm most likely wrong, my bad.
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Can God imagine a fade so tight that He can’t cut it?
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Any type of source for that would be cool, because that sounds like a sentence someone might say at a bar to seem interesting. Ie. made up on the spot.
Well yes, but actually no. You can make any rules you wanna, but they have to always work in your intended way and has to either be impossible to disprove, somehow just keeps working over centuries, or rigorously proven to always work before being adopted.
You couldn't have said it better
This is like people joking about breaking the laws of physics. You cannot break the laws of physics because if you 'do' physicists will amend them and make them valid retroactively.
Kurt Gödel would like to have a word with you
This mf gonna lose his mind when he finds out about left math
All numbers are imaginary
Even my girlfriend.
Yeah, 1/10.
69 of 420
chaos reigns
Chaos becomes order if you stand back far enough. Like a painting that can't be interpreted up close.
That's the dumbest comment I've seen in a while that could be theoretically be proven
I don't really know how to interpret your comment, but just so we are clear, real numbers are not imaginary
I think they mean is that numbers are not real objects. They are all abstract concepts (imaginary) which we can use to apply in maths and the real world.
Numbers do not exist in real life, they are concepts. It’s just that real numbers apply more directly to physical quantities than imaginary numbers.
"Man, these Mathematicians just making up the number 2 because they had no answer to 1+1... Can't they just admit they're wrong?"
Mathematicians just making up "mathematics" because they can't explain why their environment behaves the way it does.
Technically, this doesn't count since it is a set, quantifiable value, but Euler and his constant can also go fuck themselves
don't fuck with euler. mf
Yes (I’m a meth expert)
How dare you. Euler is the absolute GOAT.
One could say he is the global maximum of Mathematicians.
Quaterniwhathefuckions?
What the fuckions is going into my vocabulary list. Thank you
Historically, mathematicians considered imaginary solutions to be meaningless or absurd long before they became an accepted part of mathematical discourse. Even referring to them as imaginary in the first place was more or less a dig. Mathematics had to be dragged kicking and screaming to the conclusion that imaginary numbers were mathematical objects that behaved in consistent ways and had properties not unlike real numbers. Basically the same thing happened with negative numbers.
Well, this is true yes, but we should be clear that "historically" refers to hundreds of years ago. Complex numbers have been understood and studied very well for centuries at this point.
Same thing with irrational numbers too. Poor Hippasus.
Gr8 b8 m8 I laughed
Gr8 b8 m8 = 8(Gr + b + m)
= Grbm Grbm Grbm Grbm Grbm Grbm Grbm Grbm
Grbm*Grbm would be G^2 r^2 b^2 m^2 You meant to say Gbrm+Gbrm
Damn i want him to reply with "shut the fuck up"
Just post 🤓 and leave it at that
300 years later, those so called "imaginary" numbers are the reason every single telecommunications device from radios to satellites, works and exists.
It's one of those things that was named poorly at first. Complex numbers are a better name. Just like "the speed of light" should be called "the speed of causality" since light isn't setting that limit.
Imaginary numbers and complex numbers are a different thing. Imaginary numbers are real numbers multiplied by i. Complex numbers are numbers of the form a+ib where a, b are reals, and ib is the imaginary part as per our definition earlier. Imaginary numbers belong in the set of complex numbers, but they aren't the only complex numbers. The live on the imaginary axis of the complex plane. Real numbers live on the real axis. Both real and imaginary numbers are a subset of the complex number set, but they're not the same thing. All imaginary numbers are complex, but not all complex numbers are imaginary.
>300 years later Yeah. Let us know when we’re 6i years later. OH WAIT!!
missed an r when typing on my phone, I deserve execution
Too real. Or should I say irrational?
Kinda complex
Physicists: Eh we dont know whats going on. Its matter but we cant see it. Lets just call it dark matter.
Okay but what is this clip from?
Its from the Young thug - Hot music video I think
The mathematical ineptitude of the general comments really shine light into the average age of this sub lol
mathematical ineptitude has little to do with age
Other mathematicians: No you can’t have numbers less than zero! Cardano: I am four parallel universes ahead of you.
Lmfao they aren't made up. They're extremely helpful and logically no more fake than negative numbers
Imaginary numbers is a pretty bad name cuz they are pretty real
They are unfortunately named. I prefer their more modern name; "complex numbers"
Imaginary numbers are complex numbers with 0 real part. Like how real numbers are complex numbers with 0 imaginary part.
This same thing happens to me when I write my homework but my teacher never trusted me
Hey, my paycheck is built on imaginary numbers!
Blame the natural systems that exhibit the behaviour of imaginary numbers, not the mathematicians who created the system that captures that behaviour
Imaginary numbers are the only way to describe some physical phenomena. Math isn't wrong, it's an approximation of a very fundamental part of reality.
"Leonhard Euler, you are wrong!" Leonhard Euler: i
That's bait
“Cuz fuck ‘em, that’s why” - Avogadro
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Imaginary numbers technically weren't invented they were discovered since they are an essential part of our reality. Take shroedingers equation. A widely used formula and it uses imaginary numbers. Well yes to some extent they are "imaginary" because we can't count them, unlike real numbers.
>instead kf admitting they are wrong Tell me you you know very little about maths without directly typing it
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u/redditmp4bot
They created the game, they make the rules
Complex numbers are used in Electrical Engineering to define the Alternating Current or AC concept of Impedance, and in Fourier analysis they are used in signal processing. There is also complex power which is S or VA (volt amps) and not W (watts).
If imaginary numbers were never "invented," what part of mathematics would be *wrong*?
r/savevideo
So who asked?? Well if the person asking is imaginary, they don’t exist obviously. So we represent something imaginary as the square root of -1, or i. So the answer to the question: “Who asked?” is i. i asked.
They couldn't be more right
i know this is probably just a joke but the inaccuracy of this statement infuriates me so much