why do people take calculus seriously when Marx disproved it 250 years ago

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# why do people take calculus seriously when Marx disproved it 250 years ago

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why do people take calculus seriously when Marx disproved it 250 years ago

I am curious how people explained these things to themselves before limits. I know there’s a mathematical field today that uses infinitesimals but I’d be interested to learn how they thought about these things.

Read Euler, he is the master of us all

What’s the short version? Using series only and avoiding infinitesimals except in workable cases (differentials etc)?

>what is the shorter book between Introductio in analysin infinitorum and Institutiones calculi differentialis

The latter i think

I will not be reading an outdated book on mathematics to satisfy a curiosity I can just resolve by calling my friend who teaches a course on history of mathematics in physics… I was hoping to get an answer here and now

Euler isn't outdated. You can still teach based on his books, and his books are still better than most modern ones.

Come on. It’s outdated. For example related to this discussion, he didn’t have the modern definition of the limit.

Limits are gay.

You’re gay

Yes it should.

Why?

Because it seamlessly connects sequences and functions, moving the student from the discrete to the continuous while maintaining rigor.

They're fricking freshmen dude. All they need to know is how to use derivatives. Literally nobody gives a frick about that rigor besides professional mathematicians.

They should already know how to take derivatives from highschool. If they’re enrolled in a calculus class, they should be taught calculus. If you want to teach them remedial math, set up a different class.

They only take calculus because their major requires it. They don't need to know the e-d definitions of limits. For fricks sake dude, I'm a theoretical physicist working with qft and even I don't use that bullshit. I learned it for my math major however.

None of that has anything to do with what I wrote. I’m sure a theoretical physicist working with qft could understand basic English. Read it again.

Oh, you're the resident climate shill. You're so easy to identify.

The what? I know nothing about the climate. Stop changing the subject, moron

Yes, I know.

>Muh rigor in math

>I don't know basic science

Lmfao.

I know math, not climate science. Are you too stupid to understand the difference? Or is your degree in physics from Google university?

All that rigor and you can't even understand basic science. Sad.

Hey Mr. Theoretical quantum Physicist. Quick question: what method is generally used to calculate quantum states after the highest energy state is known?

Since you’re a big time quantum physicist you should be easily able to answer this very basic question. Thanks.

he won’t answer this lol

>what method is generally used to calculate quantum states after the highest energy state is known?

Not him but this question is extremely vague. What do you even mean by "calculate state"?

It’s an extremely specific question in basic quantum mechanics, trust me.

>It’s an extremely specific question in basic quantum mechanics, trust me.

It doesnt mean anything.

"calculate state" is a meaningless statement.

Just use google, moron

https://en.m.wikipedia.org/wiki/Quantum_state

I know what a quantum state is. However the phrase "calculate state" is meaningless.

Okay, I’ll spell it out: how do you calculate the quantum states of a two particle system based on the known eigenstates of the individual particles. Assume you know the highest energy state already and neglect interaction forces.

>how do you calculate the quantum states of a two particle system based on the known eigenstates of the individual particles.

A state can be any state in the Hilbert space of the system in consideration. What you are mentioning has no dynamics, you talk about "system" with nothing in it.

You want the initial state?

Some future state? What the frick do you want

Lmfao ok. Physicslet confirmed. Frick off larper.

Im not that anon that claimed to be a theoretical physicist.

Your attempt at shaming him backfired, you are asking absurd things that cant be answered. It only paints you as extremely ignorant

Lmao ok. It’s a cool coincidence that he disappeared once I asked my question and you immediately showed up to defend him, without the poster count going up.

What does it matter to you? Your question is still absurd. It never made any sense and you think it did because the grammar was correct.

Lol. Lmao.

Seethe dumbass

>It’s a cool coincidence that he disappeared once I asked my question a

You think only two people can read a thread?

So no answer? lmfao

Still no response.

You think people cant just get off the computer and go do something else? You might never get an answer

>Hey Mr. Theoretical quantum Physicist

It's Dr. Physicist to you, boy.

Correct.

I got other shit to do than to argue with an idiot. I check this board when I want and am not here perpetually like you.

So no answer to this basic quantum physics question that requires no calculation, just basic knowledge from third year physics? Lol

>So no answer to this basic quantum physics question

You never asked a question. "calculate state" is not a question

answer the question homie

First you have to ask a question

Just answer the question already. Jesus Christ.

you have to ask a question first

Embarrassing.

This won’t help you bro

Now can you ask that question?

obvious larper

Loser

>math, not climate science

math is not science, moronic schizo.

Well, I'm a physicist and understand both math and science. Meanwhile mathgays with all their rigor don't even understand science and have at best an equal understanding of all the important math that I do. Circlejerking over rigor doesn't improve understanding of applicable math

t. Mandlbaur

That definition shouldn't be taught in calc 1

>You can still teach based on his books, and his books are still better than most modern ones.

+1. I learned precalc from Euler's elements. Way better than anything modern

Mathematics doesn't really become dated. Its timeless. Only real difference is terminology maybe, or how something is viewed may be from a different perspective. But the concepts themselves don't fundamentally change. The methods of calculus are not any different, just the formalization justifiying the use of those methods

The methods are different. Most significant calculations in calculus are done using limits today. It’s not just formalization. Calculus without limits is like 10 times harder and some calculations are essentially impossible.

List 2 calculations that are 10 times harder without limits.

>what is hyperreals?

I will continue to use infinitesimals in a rigorus way and you can stay seething about it.

For example: f = (cos x +1)^x

Or anything similar. Much easier thru the definition

I am not against the hyperreals.

calculus was a bit informal and intuituve before it was formalized, differentials were just taken as small numbers, no one cared about formality 200 years ago

They intuitively used limits but it wasn’t formalized

that doesn't even make sense, did japanese people really fall for this?

This is basically saying fractions don't exist actually and has nothing to do with the definitions of a derivative.

there are no limits in an epsilon proof

Do you even know what the original definition of the derivative was?

Probably something geometric.

Enlighten us wise one

Wrong. It was based on infinitesimals and an intuitive idea of the limit.

Newton: “Those ultimate ratios with which quantities vanish are not truly the ratios of ultimate quantities, but limits towards which the ratios of quantities decreasing without limit do always converge; and to which they approach nearer than by any given difference, but never go beyond, nor in effect attain to, till the quantities are diminished in infinitum.” (Principia, Book 1, Section 1, Lemma 2)

Leibniz: “The calculus of differences is the science of the comparison of quantities that are infinitely small, or of the comparison of finite quantities by means of infinitely small ones.” (Nova methodus pro maximis et minimis, Introduction)

There are no such things as "infinitely small" entities. This effectively relies on an inverse notion of infinity where some quantity is smaller than any other number, no matter how small that number is in the first place. Calculating with infinities will also yield the precise contradictions that you see with zero.

This is a philosophical problem more so than mathematical. dy/dx = a makes sense when you consider it an extrapolated limit for when both dy(x) and dx approach zero. In other words, when you start putting in zeros for variables that are actually non-zero in any other situation, for example ddx or dx^2. Of course, in reality dy/dx ≈ a.

>there is no such thing as [X] entities

Not a mathematical statement. “Entities” is especially moronic lol

>dy/dx makes sense when you consider it an extrapolated limit

Limits weren’t involved in the definition of the derivative then. That’s the point. The technique was different and utilized infinitesimals but ad hoc, without formalization.

>Not a mathematical statement. “Entities” is especially moronic lol

Renders the notion of mathematics as a tool to describe physics at best problematic, doesn't it? If an entity can be infinitesimally small, what is it? Ignoring the philosophy of practical mathematics for once here, pretending that a number can be both equal and unequal to zero is just stupid.

dy/dx is just fine but dx^2 = 0?

>The technique was different and utilized infinitesimals but ad hoc, without formalization.

The strategy consisted in simply erasing any infinitesimal variable which was raised to a power higher/other than the infinitesimal variable with the lowest exponent.

>Its the slop of a curve

Well.. achtchually a single point can't have a slop which dy/dx, in essence, is.

>than with the pedantic delta epsilon shit

I insist on pedantic delta epsilon shit.

>more moronic nonsense about entities

Math isn’t you strong suit buddy. Why don’t you try a bio major?

>Math isn’t you strong suit buddy. Why don’t you try a bio major?

This does not, in any meaningful way, counter my argument, does it?

You didn’t make an argument. You gibbered incoherent nonsense. good luck with bio 101

>You didn’t make an argument. You gibbered incoherent nonsense

Yet, you're unable to explain what is incoherent about my comment. You can't make a claim and not back it up with an argument on your own side.

>Good luck with bio 101

Weak ad hominem. Shows insecurity

You’re a mathlet. I don’t consider you worthy of anything more than weak ad hominems, moron.

>something something u cant into maths go back to bio xD

I just answered for the other anon to make the discussion progress quicker.

Not him but your statement

>If an entity can be infinitesimally small, what is it?

Was indeed not an argument to begin with and displays zero understanding of mathematics and randomly introduces “what is it?” into the conversation as if it’s a valid mathematical argument. It’s not.

>Was indeed not an argument to begin with and displays zero understanding of mathematics and randomly introduces “what is it?” into the conversation as if it’s a valid mathematical argument. It’s not.

True, I'll give you that.

>a single point can't have a slop

You are denying reality in the same type of absurdism as the paradox of Zenon. Its obvious that any smooth and continuous curve has a slope, barring some pathological gotcha fractal curves.

Everyone understands this and you are not smarter for being a contrarian. Its just the slope of a curve. Draw a little triangle to calculate it on paper.

>Its obvious that any smooth and continuous curve has a slope

Again, I'm not concerned with the practical implications here.

>Everyone understands this and you are not smarter for being a contrarian

But how does this relate to my concern here? Either admit that we're talking about limits with the differential translating into an extrapolation of the limit for n approaching 0 or keep mischaracterising it as something that it is not.

>no one said infinitesimals are zero, you are just extremely stupid.

Yet, dx^2 is 0, but dx isn't? So, why are we writing dy = adx and not dy = adx+bdx^2 etc.?

Do you actually not understand limits or you are just an autism upset that 17th century mathematics was less rigorous than 19th century mathematics?

>Yet, dx^2 is 0, but dx isn't?

dx =/= https://en.wikipedia.org/wiki/Dual_numbe r=/= https://en.wikipedia.org/wiki/Nonstandard_analysis

>Zenon

ain't that some anime villain?, or was it a mecha anime's alien empire?

>can be both equal and unequal to zero is just stupid.

no one said infinitesimals are zero, you are just extremely stupid.

>still getting filtered by dual numbers in 2024

Are you stupid? Its the slop of a curve

extremely easy and intuitive concept. People have a much easier time with informal limits and the idea of an infinitesimal as a small number than with the pedantic delta epsilon shit

>there are no limits in an epsilon proof

The modern definition of the limit uses the “epsilon-delta” method. That’s what the guy was saying. Are you moronic?

>Are you moronic?

Are you?

Epsilon-delta predates limits, that's how they did it before limits.

Epsilon delta is how they did what?? How would they explain the concept of “numerator is zero, denominator is zero, but ratio isn’t” using epsilon delta you dense moronic frick

>Epsilon delta is how they did what??

Explain derivatives you moron

No it wasn’t moron. They used infinitesimals.

>infinitesimals

no such thing

>no such thing

Not a mathematical statement. If I define it, and it works, it’s math. moron.

>and it works

You’re welcome

https://homepage.math.uiowa.edu/~stroyan/InfsmlCalculus/Lecture1/Lect1.pdf

If you cant even format your sum correctly it's not rigorous

>mathlet confirmed

Frick off

>infinitesimals

>setting value to 0

Choose one

It was ad hoc. They had no formalization. That’s what Marx is pointing out here

It's called pulling shit out of your ass

Okay. And it was the beginning of modern calculus lol. Get fricked loser

>And it was the beginning of modern calculus lol

And alchemy was the beginning of modern chemistry

>newton’s invention of calculus was like alchemy

moron detected.

Newtons formulation was about as rigorous as alchemy, yes

He was just lucky it worked

Lol okay now read what Newton actually said

I don't think you understand how rigor works, commie

I don’t think you understand mathematics if you think Newton was “lucky”, moron. Now go talk to your fellow humanities scholars about how Newton was a white racist man

I see, the commie is projecting

Newton was a fraud

its the slope of a curve

That’s a geometric definition, not an algebraic one.

>not an algebraic one.

So what?

So you can’t use it to calculate the derivative of a given function plus non-smooth functions with derivatives exist

>So you can’t use it to calculate the derivative of a given function

Yes you can, just draw it and get your set of rulers

>plus non-smooth functions with derivatives exist

This pedantry isnt doing you any favors. But to keep it short "the exception proves the rule"

>just draw it

Absolute mathlet take lmao

Whats wrong with drawing?

drawing will allow you to calculate the derivative at a point, maybe a few points, not give you the derivative as a function. For example: try to calculate the derivative of f(x) = 5x^7 +7x^ 4 -x^2 by drawing. You’ll never get it. But algebraic methods yokels the derivative as a function of x in seconds.

>drawing will allow you to calculate the derivative at a point, maybe a few points

So what?

You’re asking me why knowing the instantaneous derivative is important in math?

At least it doesn't rely on infinitesimals to define a differential

Are you asking why the instantaneous derivative is important in mathematics? Yes or no?

Yes. Who really needs an exact value? We can basically just look at the graph and count boxes and that's really good enough. Just approximate using newton's method. Keep computing until you're happy

Mathlet morons

>he said, building the foundations of math on sand

Shut up, mathlet.

He didn’t say an exact value. You can’t get a derivative function by counting boxes. So if you want the derivative function to carry out further manipulations on it, you can’t just count boxes

depends how many points I want and how small of an error I want. If I want a LOT of points with low error, a computer becomes useless at some point.

>depends how many points I want and how small of an error I want. If I want a LOT of points with low error, a computer becomes useless at some point.

Just get a better pc lmao

>can’t into numerical analysis

Lol

>can't into money

typical poor mathgay

I’m in physics actually

A computer can tell you the derivative of a function instantly by just checking the slope

>dx=0

>dy=0

This is the equivalent of writing a paper to justify why you don't know how chemical bonds work because you never attended classes.

Karl Marx was the first black mathematician.

Damn now this is a legendary shitpost. You don't have to write a socioeconomic fanfic series, half a page is enough

Why do people take Marx seriously when he failed to understand calculus 250 years ago?

Blaming all your problems on other people just feels good man. There's a special kind of emotional state you can achieve feeling completely free of any responsibility for your circumstance combined with a deep envy of all those who are better off in anyway that's just magical.

It's like knowing you're a god and a bunch of moronic apes have wronged you. You're a perfect being and in time they'll all get theirs. It perpetuates itself and it's intoxicating.

So Marx is moronic. We already know that.

>moronic schizo LARPer can't even answer anons question

we might as well be talking to a bot...

In every non-anglo and non-anglo-adjacent country they teach mathematicians, physicists and engineer Real Analysis, not that watered down calculus bullshit.

I have a degree in Computer Engineering and when I got to the US for my PhD I discovered that the 4th year undergrad engineering students don't even know what the Lebesgue measure is or how you prove the implicit function theorem lmao

Can confirm, I'm from south america, first year undergrad physics, first two math classes are analysis.

>, first year undergrad physics,

Black person you are like a worm

Bibliography is apostol, spivak, and (extracurricular) rudin.

i never liked the notation, it made it hard to learn when you moved on from algebra

Why would dx, dy be zero?

What does dx equal?

I only know the definition from limits. dx approaches 0 and dy equals f(x+dx)-f(x) as dx approaches 0.

https://encyclopediaofmath.org/wiki/Differential

ITT: mostly people who think math was the same some 200 years ago

>Marx

you are a cultists

this is very funny cause everyone is tripping over themselves trying to dunk on Marx with this one, when it was never published (its on a private letter he wrote to someone whining about math books he was studying), he's actually complaining about the notation (he's correct, Leibnitz's is better), and later mail shows he probably had someone explain it to him and he moved on. Imagine the world's dumbest people (twitter users) are trying to prove they are smarter than you by dunking on your writing on your study notes after you die

Most people here get what he’s saying and aren’t really dunking on him. It’s still funny to read

they should, he created a cult

I can't into math, but how is 0 = 0 supposed to be a contradiction? Wouldn't he have to show that 0 != 0 to prove a contradiction?

The contradiction is that “a” can now take any value, since it will always satisfy this “equation”. But we assumed it is a specific value. Contradiction.

That's not true, the (You) isnt linked also that would be me not you. wtf are you trying to pull idiot?

This whole thread is 1 deranged lunatic talking to himself. Poster count didnt increase and he even admitted to it