/sci/ - Science & Math » Thread #13770428

89KiB, 400x400, brainletfilter.png

View Same Google iqdb SauceNAO

Anonymous Wed 20 Oct 02:59:56 2021 No.13770428 View Reply Original Report

Quoted By: >>13770443 >>13770446 >>13770487 >>13770716 >>13770748 >>13770966 >>13771219 >>13771238 >>13772773 >>13773059 >>13773297 >>13773427 >>13774400 >>13774687 >>13775045 >>13775368 >>13776620 >>13777784

This is not a ratio and if you treat it as such you are a brainlet.

This is an operator ("d/dx") acting on a function (y)

("dy") is not a distance because it is not a number, you can not calculate an "infinitesimal" and if you think of it as "rise over run" you are a stupid brainlet, it is an infinitessimal lipschitz constant

Anonymous

Anonymous Wed 20 Oct 2021 03:02:46 No.13770434 Report

Quoted By:

cum on my face sir

Anonymous

View Same Google iqdb SauceNAO smug bitch pwnd ur url.jpg, 21KiB, 360x318

Anonymous Wed 20 Oct 2021 03:04:41 No.13770442 Report

Quoted By: >>13770508 >>13770809

>This is not a ratio and if you treat it as such you are a brainlet.

Anonymous

Anonymous Wed 20 Oct 2021 03:06:16 No.13770443 Report

Quoted By: >>13770461 >>13771056

>>13770428
How do you integrate a function then, faggot?

Anonymous

Anonymous Wed 20 Oct 2021 03:07:12 No.13770446 Report

Quoted By:

>>13770428
it is the limit of the ratio

Anonymous

Anonymous Wed 20 Oct 2021 03:09:03 No.13770454 Report

Quoted By: >>13770467 >>13774563

You are not a woman and if you think you are, you are mentally ill.

You are a man ("xy") acting like a woman (xx)

("op") is not a woman because you have no womb, you have no ovaries, you have no eggs and if you think of it as a "real vagina", you are mentally ill. it is an axe wound.

Anonymous

Anonymous Wed 20 Oct 2021 03:10:02 No.13770456 Report

Quoted By: >>13770460

It's both an operator and a ratio seeing as how it's a rational composition.

Anonymous

Anonymous Wed 20 Oct 2021 03:11:08 No.13770460 Report

Quoted By: >>13770488

>>13770456
then again a ratio really is an operator anyways.
which means simply, it's a ratio

Anonymous

Anonymous Wed 20 Oct 2021 03:11:42 No.13770461 Report

Quoted By:

>>13770443
have you never heard of polygons ? brainlet

Anonymous

Anonymous Wed 20 Oct 2021 03:12:43 No.13770467 Report

Quoted By:

>>13770454
basado

Anonymous

Anonymous Wed 20 Oct 2021 03:17:13 No.13770487 Report

Quoted By:

>>13770428
Leibniz originally envisioned derivatives as the quotient of an infinitesimal change in y by an infinitesimal change in x. Derivatives have moved away from that definition and towards it's modern limit definition, but they seem to work very similar to quotients for the majority of basic applications of calculus, which is why it's easy to mistake it for a quotient for most people who have never taken analysis.

Anonymous

Anonymous Wed 20 Oct 2021 03:17:35 No.13770488 Report

Quoted By: >>13770504

>>13770460
>then again a ratio really is an operator
what does a ratio operate on? what's its domain and codomain?

Anonymous

Anonymous Wed 20 Oct 2021 03:20:36 No.13770504 Report

Quoted By:

>>13770488
>being this much of a brainlet

Anonymous

Anonymous Wed 20 Oct 2021 03:21:24 No.13770508 Report

Quoted By:

>>13770442
>tfw no smug bully gf that violates you intellectually every night

Anonymous

Anonymous Wed 20 Oct 2021 04:35:58 No.13770716 Report

Quoted By: >>13770966

>>13770428
Claim: you can treat dy/dx as a ratio.
Proof: let $z = \frac{dy}{dz} \def \lim_{\Delta x \to 0} \frac{\Delta y (\Delta x)}{\Delta x} = \frac{\lim \Delta y}{\lim \Delta x}$
Which implies we may write
$z \lim \Delta x = \lim Delta y$
Which finally suggests, passing the limit to differentials that z dx = dy.
QED fag

Anonymous

Anonymous Wed 20 Oct 2021 04:49:29 No.13770748 Report

Quoted By:

>>13770428
>what is nonstandard analysis

Anonymous

Anonymous Wed 20 Oct 2021 05:15:15 No.13770809 Report

Quoted By:

>>13770442
Spot on hahaha

Anonymous

Anonymous Wed 20 Oct 2021 06:34:01 No.13770966 Report

Quoted By:

>>13770428
>>13770716
I seethed at everyone’s lack of rigor when I did Cal myself. It can be thought of as a manipulatable functor (in the sense of an operator that returns a function). Manipulating it so that dy and dx are on the same side (and things like that) is valid and the equals stays correct across integration when both sides have the right operator under the transformation. There’s no lack of rigor in the Leibnizian notation, only a lack of appreciation for rigor.

Anonymous

Anonymous Wed 20 Oct 2021 07:31:14 No.13771056 Report

Quoted By: >>13775356

>>13770443
Tai's method

Anonymous

Anonymous Wed 20 Oct 2021 08:50:35 No.13771219 Report

Quoted By:

>>13770428
>This is not a ratio
...bcoz it is the *limit* of a ratio.
>This is an operator
No.
It may be thought of as the *result* of an operator.
Lrn2calculus fgt pls

Anonymous

Anonymous Wed 20 Oct 2021 08:58:13 No.13771238 Report

Quoted By: >>13771243

>>13770428
it's a ratio of differential forms

Anonymous

View Same Google iqdb SauceNAO this-motherfucker-knows.png, 155KiB, 459x306

Anonymous Wed 20 Oct 2021 08:59:07 No.13771243 Report

Quoted By:

>>13771238

Anonymous

Anonymous Wed 20 Oct 2021 19:19:35 No.13772773 Report

Quoted By: >>13772955

>>13770428
Correct.
>non standard analysis
Fucking useless shit made up by a neurotic Jew.
>ratio of differential forms
Not in elementary calculus.

It really is just a notation for a derivative. Manipulating them as ratios can give correct answers sometimes, and erroneous results in others.

Anonymous

Anonymous Wed 20 Oct 2021 20:33:02 No.13772955 Report

Quoted By: >>13773035

>>13772773
it's a ratio of differential forms

Anonymous

Anonymous Wed 20 Oct 2021 20:57:41 No.13773035 Report

Quoted By: >>13773058 >>13773111 >>13773323

>>13772955
>not in elementary calculus
Seems you missed this part. Treating it as a ratio of infinitesimals in the context of elementary calculus can and will lead to erroneous results. Further results in differential geometry allow you to treat it as a quotient of differential forms. This is not something someone beginning studies into elementary calculus should be concerned with.

Anonymous

Anonymous Wed 20 Oct 2021 21:04:00 No.13773058 Report

Quoted By: >>13774198

>>13773035
it's still a ratio of differential forms

Anonymous

View Same Google iqdb SauceNAO 1595863074227.jpg, 22KiB, 1288x305

Anonymous Wed 20 Oct 2021 21:04:10 No.13773059 Report

Quoted By:

>>13770428
What are you talking about? The math works out when you treat it as a ratio

Anonymous

View Same Google iqdb SauceNAO Kord-machine-gun.jpg, 201KiB, 782x702

Anonymous Wed 20 Oct 2021 21:18:16 No.13773110 Report

Quoted By:

Ze ist nich ratio but ein limit of zuch. Zerefore ze hast many properties of ein ratio and thus Leibniz notation is zustified.

T. Top euro mathfag

Anonymous

Anonymous Wed 20 Oct 2021 21:18:25 No.13773111 Report

Quoted By: >>13774198

>>13773035
>Treating it as a ratio of infinitesimals in the context of elementary calculus can and will lead to erroneous results
That seems meaningless. Can you clarify by presenting an example?

Anonymous

Anonymous Wed 20 Oct 2021 22:05:46 No.13773297 Report

Quoted By:

>>13770428
I agree,
but then, why does the infinitessimal notation account rightly for physical units in physics equations ?

Like in mechanics,

work = integral( force * dl)

work is kg?m2?s?2
force is kg.m.s-2
dl is m

and it checks out,

kg?m2?s?2 = kg.m.s-2 * m

Anonymous

Anonymous Wed 20 Oct 2021 22:11:24 No.13773323 Report

Quoted By: >>13774198

>>13773035
>Treating it as a ratio of infinitesimals in the context of elementary calculus can and will lead to erroneous results.
It does not for the first derivative. Second derivatives can, and that is because the notation for it doesn't actually represent the right expression.

Anonymous

View Same Google iqdb SauceNAO chain rule.png, 4KiB, 423x172

Anonymous Wed 20 Oct 2021 22:37:24 No.13773427 Report

Quoted By: >>13773634 >>13774238

>>13770428
Looks like a ratio to me.

Anonymous

Anonymous Wed 20 Oct 2021 23:22:43 No.13773634 Report

Quoted By: >>13773741

>>13773427
That's chain rule not algebraic cancelation of the numerator and denominator

Anonymous

Anonymous Wed 20 Oct 2021 23:37:06 No.13773741 Report

Quoted By:

>>13773634
cope

Anonymous

Anonymous Wed 20 Oct 2021 23:42:29 No.13773784 Report

Quoted By: >>13773817

can someone show me ONE (1) example where using it as a ratio doesn't work.

give me a function f(x)

Anonymous

Anonymous Wed 20 Oct 2021 23:46:39 No.13773817 Report

Quoted By:

>>13773784
>give me a function f(x)
f(x)=ass+YWNBW

Anonymous

Anonymous Thu 21 Oct 2021 00:54:30 No.13774198 Report

Quoted By: >>13774455 >>13774516

>>13773058
And you are still a dumb nigger who doesn’t realize that the same symbol can mean totally different things in different contexts.

>>13773111
Sure. Take (dx/dt)^2. If you treat the notation as a ratio and apply standard algebraic manipulation, then that statement would be equivalent to (dx^2)/(dt^2), which looks similar to Leibniz notation for the second derivative. This is of course wrong. To make matters worse, manipulating the notation as a ratio seems to actually work in some ways. In these situations, there is usually the chain rule or u-substitution hiding somewhere.

>>13773323
Yes it does for the first derivative, see my example above.

Anonymous

Anonymous Thu 21 Oct 2021 01:01:14 No.13774238 Report

Quoted By: >>13774270

>>13773427
Because it's a fucking coincidence for this particular situation.

Anonymous

Anonymous Thu 21 Oct 2021 01:11:08 No.13774270 Report

Quoted By:

>>13774238
>coincidence

Anonymous

Anonymous Thu 21 Oct 2021 01:38:39 No.13774400 Report

Quoted By:

>>13770428
If it's not a ratio then why does using it as one work so well?

Anonymous

Anonymous Thu 21 Oct 2021 01:50:04 No.13774455 Report

Quoted By: >>13774474

>>13774198
>Sure. Take (dx/dt)^2. If you treat the notation as a ratio and apply standard algebraic manipulation, then that statement would be equivalent to (dx^2)/(dt^2), which looks similar to Leibniz notation for the second derivative. This is of course wrong.
$\frac{\mathrm{d}x^2}{\mathrm{d}t^2}$ is not $\frac{\mathrm{d}^2 x}{\mathrm{d}t^2}$ , so you have not demonstrated anything.

Anonymous

Anonymous Thu 21 Oct 2021 01:54:41 No.13774474 Report

Quoted By: >>13774544

>>13774455
And (dx/dt)^ is still not (dx^2)/(dt^2), so you have further demonstrated you are a brainlet.

Anonymous

Anonymous Thu 21 Oct 2021 02:02:23 No.13774516 Report

Quoted By: >>13774544

>>13774198
treating dy/dx as a ratio always works because it actually is a ratio of differential forms

Anonymous

Anonymous Thu 21 Oct 2021 02:05:54 No.13774544 Report

Quoted By: >>13774629

>>13774474
>further
This is my first post in this thread.
>And (dx/dt)^ is still not (dx^2)/(dt^2)
The argument you gave in your post was that, granting that Leibniz's notation can be manipulated as a fraction, (dx/dt)^2 would be equal to (dx^2)/(dt^2). Then you made the implication that this is somehow a contradiction, because (dx^2)/(dt^2) "looks similar to Leibniz notation for the second derivative." It is "of course wrong" that (dx/dt)^2 is d^2 x/dt^2, but that doesn't mean that (dx/dt)^2 is not (dx^2)/(dt^2). as I said, your line of reasoning did not demonstrate anything.

>>13774516
Differential forms in general do not constitute a field. This only works in one dimension.

Anonymous

Anonymous Thu 21 Oct 2021 02:08:32 No.13774563 Report

Quoted By: >>13774575

>>13770454
How is it an axe wound? Did some guy swing an axe into another guy's genitals as some experiment to increase whole-body airflow?

Anonymous

Anonymous Thu 21 Oct 2021 02:10:30 No.13774575 Report

Quoted By:

>>13774563
Yes. The experiment yielded positive results.

Anonymous

Anonymous Thu 21 Oct 2021 02:24:11 No.13774629 Report

Quoted By: >>13774701

>>13774544
Ok fuck face. Let me put this another way. Lets say you have not defined dx and dt as differential forms, and instead think of them as infinitesimals, which is how the notation originated. In this case the term infinitesimal is simply a concept. It is not formally defined, and so you cannot manipulate the infinitesimals as variables according to the standard rules of algebraic manipulation. This is implicit in my earlier statements but since you are a midwit you do not understand this. This was the entire motivation for non standard analysis: to develop a more rigorous treatment of infinitesimals so they can be manipulated. Back to the example, squaring a derivative and then stating it is equivalent to the quotient of squared infinitesimals has no meaning without a rigorous treatment of infinitesimals. I only stated it looks similar to second derivative notation to demonstrate that an untrained person or new student in calculus could come to wrong conclusions or become confused when treating it as a ratio.

Anonymous

Anonymous Thu 21 Oct 2021 02:47:16 No.13774687 Report

Quoted By:

>>13770428
Are you my high school Calc 1 teacher?

Anonymous

Anonymous Thu 21 Oct 2021 02:51:09 No.13774701 Report

Quoted By: >>13775044

>>13774629
>without a rigorous treatment of infinitesimals
You should not be doing this.
>an untrained person or new student in calculus could come to wrong conclusions or become confused
Skill issue.

The point stands that you CAN treat derivatives as a ratio, you shouldn't care about "elementary calculus" because it has no bearing on how you can treat derivatives, and OP is a nigger.

Anonymous

View Same Google iqdb SauceNAO 4eeabe53efba0421300bd95c8332c7c9.png, 3MiB, 2337x1434

Anonymous Thu 21 Oct 2021 04:05:41 No.13774843 Report

Quoted By: >>13775065

The first derivative can be arranged all you want by the rules of algebra. The second derivative is the one that causes errors because it's not the right formula (at least for this purpose). Look at solving first-order ODEs by separation of variables. It's rigorous.

Anonymous

Anonymous Thu 21 Oct 2021 05:38:17 No.13775044 Report

Quoted By:

>>13774701
>You should not be doing this
I agree. NSA doesn’t do anything “standard” analysis can’t. It was developed to satisfy some neurotic jew’s obsession with Leibniz.

>you CAN treat derivatives as a ratio
I guess we’ll have to agree to disagree. I personally think of them as a limit of a ratio, but I do not see Leibniz notation as a true ratio. I am not concerned with differential forms when I say this. I am saying this with respect to the history of calculus and Leibniz notation in particular.

Anonymous

View Same Google iqdb SauceNAO 142137910_2732594470387672_26994 (...).jpg, 21KiB, 320x321

Anonymous Thu 21 Oct 2021 05:38:58 No.13775045 Report

Quoted By: >>13775070

>>13770428
I treat differentials as numbers multiplying by dx on both sides and simplifying them when needed. And no mathcuck can stop me.

Anonymous

Anonymous Thu 21 Oct 2021 05:47:54 No.13775065 Report

Quoted By:

>>13774843
Separation of variables is more a helpful problem solving tool rather than a justified mathematical operation. There is u-substitution hiding in the background that provides its justification. Even then, if it’s stupid, but it works, then it’s not stupid.

Anonymous

View Same Google iqdb SauceNAO 38571844-F097-459B-A9ED-360F196A (...).jpg, 10KiB, 163x175

Anonymous Thu 21 Oct 2021 05:50:24 No.13775070 Report

Quoted By:

>>13775045
Very well said friend. I also treat infinity as a number along with infinitesimals. So 4 infinity divided by 2 infinity is 2! See? Because the infinities cancel!

Anonymous

Anonymous Thu 21 Oct 2021 08:00:37 No.13775356 Report

Quoted By:

>>13771056
Kek

Anonymous

Anonymous Thu 21 Oct 2021 08:06:45 No.13775368 Report

Quoted By:

>>13770428
How about you lipschitz my penis, fagget.

Anonymous

Anonymous Thu 21 Oct 2021 09:50:53 No.13775566 Report

Quoted By: >>13775579 >>13776810

>Ctrl+F "keisler"
I'm very disappointed in you people

EVERYONE IN THIS THREAD GO FUCKING
R E A D K E I S L E R
E
A
D

K
E
I
S
L
E
R

https://people.math.wisc.edu/~keisler/calc.html

Anonymous

Anonymous Thu 21 Oct 2021 10:00:04 No.13775579 Report

Quoted By:

>>13775566
why?

Anonymous

Anonymous Thu 21 Oct 2021 18:28:35 No.13776620 Report

Quoted By:

>>13770428
>dy/dx
>d/d * y/x
>d/d = 1
>1 * y/x
>y/x
Now you can easily divide this. You're welcome, anon. Good luck on your homework.

Anonymous

Anonymous Thu 21 Oct 2021 19:30:51 No.13776810 Report

Quoted By:

>>13775566
>drops some random faggot's name without elaborating
no I don't think I will

Anonymous

Anonymous Thu 21 Oct 2021 20:33:57 No.13776955 Report

Quoted By:

Lol that's pathetic
> you can not calculate an "infinitesimal"

Anonymous

Anonymous Thu 21 Oct 2021 23:14:48 No.13777335 Report

Quoted By:

"you cannot calculate an infinitesimal"
someone knows nothing about mathematics

Anonymous

Anonymous Fri 22 Oct 2021 02:03:13 No.13777681 Report

Quoted By:

"dy/dx is not a fraction" is something they tell you in high school to make sure the lowest common denominator doesn't get confused, it literally is a fraction, the dx at the end of the integral is literally multiplying as well, its not just notation (although brackets do get left out for convinience, other than that its literally multiplying by dx)

Anonymous

View Same Google iqdb SauceNAO __motoori_kosuzu_touhou_drawn_by (...).jpg, 952KiB, 1200x1200

Anonymous Fri 22 Oct 2021 02:36:45 No.13777784 Report

Quoted By:

>>13770428
>infinitesimal Lipschitz constant
No it fucking isn't, what are you, stupid?
First of all, Lipschitz constants are always positive.
Secondly, even if $f'(x_0)$ is non-negative, there isn't necessarily a neighnorhood of $x_0$ where $|f(x)-f(x_0)| \leq f'(x_0) | x - x_0|$ .

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches