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/sci/ - Science & Math

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12766015 No.12766015 [Reply] [Original]

"...plus a constant, you stupid faggots..."

>> No.12766025

>>12766015
Well, isn’t it always a determined percentage of the total amount ?

>> No.12766062

>>12766025
I thought it's a joke on https://en.wikipedia.org/wiki/Constant_of_integration

Like, she's listening to a conversation where people forget the plus c

>> No.12767344
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12767344

>>12766015
"I just assume the constant to be zero"

>> No.12767378

>>12766015

indefinite integrals have no place in serious maths, they don't even have a concrete definition.

>> No.12767386

>>12767378
>they don't even have a concrete definition.
??? pardon my abrupt question, but are you a brainlet?

>> No.12768248

>>12767386

Go ahead, give me a well-definition.

I have never seen a proper setup for it in a text. The proper way would be to define an indefinite integral as a set of functions then define arithmetic between them. This is never done because indefinite integrals are just shorthand and not used in any serious capacity.

You get those "paradoxes" involving the constant of integration. Really, what's going on there is that you're seeing the shittiness of its usual "definition".

>> No.12768263

>>12768248

to add, when have you ever seen a set written as set = constant + something that varies. We don't exactly write R = x where x is any real number.

>> No.12768342

>>12768248
the set of all primitive functions

>> No.12768347

>>12767378
Bro, they're called antiderivatives and they are used all the time in serious math.
>>12768248
Look up any text on calculus (for example, spivak).

>> No.12768368

>>12768347

An antiderivative is something that differentiates to a given function.

Spivak doesn't seem to mention the indefinite integral anywhere and deals with definite integrals throughout.

>> No.12768384

>>12768368
A function f is an antiderivative of g if f' =g.
People usually don't write the definition because it's so intuitive and easy.

>> No.12768385

>>12768342

Yeah that's obviously the most sensible answer. The problem is that indefinite integrals result in all sorts of notational annoyances, particularly since we insist on dropping the {}, the usual notation for sets, which results in nonsense identities. For example: https://math.stackexchange.com/questions/2308602/integration-of-frac1x-lnx-by-parts..

There's a reason you're not going to find indefinite integrals in analysis textbooks and so on.

>> No.12768403

>>12768385
The same is done with analytics.
x+o(x^2) denotes a multitude of functions.

>> No.12768408

>>12768385

And since indefinite integrals are shorthand in the first place, dropping the constant, like writing "[math]\int f' = f[/math]" isn't really going to be misunderstand. Seems a bit funny to be anal about loose notation.

Of course, if you're like solving a DE and you drop a constant that's just incorrect.

>> No.12768423

>>12768403

I may be misunderstanding but I'd read f(x) = x + o(x^2) as "for each x, f(x) is equal to x plus some error term that grows at most as fast as x^2". There are many functions f satisfying this but I have only described one.

>> No.12768431

>>12768423

To ensure well-definedness I'd give another definition of f beforehand, since as I said it doesn't uniquely define f.

>> No.12768460

>>12768385
do you know what a quotient space, quotient group etc. is?

>> No.12768463

>>12768408

(also the notation can obfuscate the nontrivial fact that f' = g' if and *only if* f = g + C for a constant C)

>> No.12768471

>>12768460

ye

>> No.12768483

>>12768471
are you also opposed to writing x + W, x + ker f etc.? do you find the notation ambiguous?

>> No.12768514

>>12768483

no I'm not against addition/multiplication etc. of sets. They are usually afforded definition/explanation when first introduced though, and that's my main issue.

I 100% have a problem with the notation [math]\int F = f + C[/math], since the LHS is ostensibly a set, and the RHS is seemingly a specific function. That mainly causes confusion with the "arbitrary constant" like the MSE post above.

To clarify, it's not hard to get a proper setup, I pointed out that a proper setup is not often used. It's a gripe that lingers over me.

>> No.12768519

>>12768514
>∫F=f+C

fuck, [math]\int f = F + C[/math] lol, can't even get that right.

>> No.12768585

>>12768514
OP in that link made the mistake of deducing C = B from A∪B = A∪C. him not understanding the definition doesn't make it faulty. the equality before he writes 0=1 is fine, he just can't "cancel" the integrals in the same way one cannot cancel W in x+W = y+W. also, you're free to dislike a notation, but you've started with saying that indefinite integrals don't even have a concrete definition. that's just not true.

>> No.12768606

>>12768514
but if you accept the notation for quotient spaces, just pretend that the "C" stands for the kernel of the differentation operator (because that's what it actually is anyway, and in general it's not even "+C" but "+C(x) where C(x) is a locally constant function")

>> No.12768639

>>12768606

yeah I suppose you're right