Dumb questions thread

>>8129288
yes

>>8129288
>Are vectors entities that can only be described in retangular coordinates?

No.

>>8129318
my answer was for your second question

>>8129288
maybe

I don't know

it's called polar coordinates, they are completely valid, and in some cases more useful than rectangular/Cartesian coordinates, because you can describe rotations

>>8129339
>>8129349
fuck off back to /reddit/

Check out curvilinear coordinates for a basic introduction. Polar coordinates are an example that should be familiar. Vectors aren't defined by a coordinate system, but can be described by coordinates. If you really want to develop a better understanding for what's a vector and what's just something with components, you'll need to crack open an intro book to differential geometry or smooth manifolds (John Lee's book is great). If you're concerned with application, a classical mechanics text will do well near the SR/GR section.

>>8129288
Yes. This is called unit vector notation.

>>8129288
You have to be 18 to post on 4chan you know

>>8129358
you can still have unit vectors with rectangular coordinates

>>8129288
vectors can be described in any coordinate system you like.
the coordinates don't even have to be linearly independent.. it's just most useful if they are.

File: 25.png (12KB, 573x168px) Image search: [Google]

12KB, 573x168px

Using Bernoulli I get x = (1/2)^[1/(n+1)]

which seems retarded but it does solve it.. help

>>8129383
Assuming that's correct, you found a constant solution.
Follow the hint and consider what the chain rule tells you about the left hand side after the suggested multiplication. (Compare to what you'll have on the right hand side to pick a new variable)

>>8129376
>>8129358
>>8129353
>>8129318
But wouldnt "a" have unit while "b" would be unitless? If i make a dot product of that vector with itself, wouldnt it result in a sum of two things with different units? thanks in advance

how much training in logical training would I need to understand Gödel's Incompleteness Theorem?

I know BASIC set theory, we had some in calculus
but the symbols in the proofs look like hieroglyphics to me
any free resource?

>>8129362

You gonna call the police?

>>8129288
What you wrote in that picture is a tangent vector. Which means it is actually takes the form of a map [math] \nu :C_{M,p}^\infty \to \mathbb{R} [/math].

can someone describe Gauss's Law to me in layman's terms, and an example of its use?

>>8129451
>But wouldnt "a" have unit while "b" would be unitless?
a is units, b is units/radian

>>8129288
Not entirely sure this is what you're looking for but read up on Dirac Bra-Ket Notation.

https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation

>>8130004
I fucking love bra-ket, don't get me wrong, but,
>elementary question about vectors
>here, go read about matrix mechanics
????

>>8129525
I'm lost.
That's a [math] v [/math] not a [math] \nu [/math]
And you end up with something [math] \to \mathbb{R}^n [/math] (prob n=3)?
Does [math] C^\infty [/math] the family of smooth functions?

>>8129462
Start by reading "How to Prove It"

>>8129954
The way an electric field moves away from a given charge density, is proportional to that charge density.

>>8130033
It's not a map to R^3 it's a map to R and yes it is the space of smooth functions.

>>8130033
>And you end up with something...

No you don't understand. An element of [math]{\mathbb{R}^n}[/math] should be interpreted as a map of this type because [math] {T_p}{\mathbb{R}^n} \cong {\mathbb{R}^n}[/math].


> the family of smooth functions?

[math] C_{M,p}^\infty = \coprod\limits_{U \ni p} {C_M^\infty \left( U \right)} / \sim [/math]. Where [math] {C_M^\infty \left( U \right)} [/math] is the set of smooth functions [math]f:U \to \mathbb{R}[/math] and [math] \sim [/math] is two functions being equal when restricted to some neighborhood of the point p.

>>8129288
Spherical and cylindrical coordinates are very basic and common.

>>8129288
Yeah, you can have a vector as written above. The most intuitive way to think about a vector is in ractangular coordinates where each element encodes a magnitude in a dimension (thereby giving rise to slopes in each direction). You can also use vectors to encode polar coordinates, spherical coordinates, any of the previous examples including an element in the time dimension, etc. Basically, vectors are just matrices with either height or width of 1 and are used to concisely hold information.

For an interesting look at the beginning of this look at the Kahn Academy lessons in linear algebra (specifically when he starts going over changes in basis, where your vectors can be composed of a linear combination of vectors (where the standard basis is [1, 0, 0, ... , 0], [0, 1, 0, ... , 0], [0, 0, 1, ... , 0], ... , [0, 0, 0, ... , 1])). This doesn't touch on different coordinate systems, but it begins to lay the groundwork.

>>8130268
Note also that this is categorical direct limit.
i.e. [math]C_{M,p}^\infty = \mathop {\underrightarrow {\lim }}\limits_{U \ni p} C_M^\infty \left( U \right)[/math]

>>8129288
Here OP, improve the mind.
https://en.wikipedia.org/wiki/Curvilinear_coordinates

>>8130268
Why do you need all this to explain to them that a vector can be written in terms of any basis of the vector space? Isn't this all, a bit of a show-off?

>>8132035
>Isn't this all, a bit of a show-off?
Yes. You get used to ignoring the pompous math majors responding to pre-college questions.

>>8132035

Not at all. OP's question is surprisingly deep. I think it's impossible to really understand what's going on without a solid understanding of sheaves of germs of smooth functions. Given a smooth manifold (the smoothness not being essential; we could just as well consider the C^k case), we may consider a local splitting of the tangent bundle into a direct sum of line bundles. Choosing a non-vanishing section of each constituent line bundle, we may express each section of the tangent bundle as a unique linear combination of these sections of the constituent bundles. Specializing to the manifold R^2-0 yields the situation in the OP, modulo some trivial and self-explanatory notational differences.

>>8129288
Coordinate systems and vectors are studied extensively in Vector Calculus and Mulivariate calculus. This isn't really a dumb question at all.

>>8132079
If OP is unaware of anything but rectangular coordinates, OP has no fucking clue what any of those words mean, you fucking oblivious tool.

>>8132079
OP here, I'm still in doubt, if I were to write a position vector in polar coordinates, would the first component be the radius and the second an angle? How can them have different units?

>>8132085
wow please help poor OP here, thats my only question, I know about the existence of curvilinear coordinates, I've done vecotr calculus still I have a huge gap..

I just want to know how to write a position vector in polar coordinates for example... would a componente be the radius and the other an angle?? or radius times angle?? idk

>>8132107
cant be angle, units wont match, pls 4chen

File: CodeCogsEqn (4).png (2KB, 229x85px) Image search: [Google]

2KB, 229x85px

>>8132110
>>8132107
>>8132085
Please OP asked the wrong question, just point me the right one or a new one if both are wrong

>>8132085
I answered you here: >>8129975

>>8132123
so if i have a particle with the following position: (r,theta)= (1, pi) my vector would be
[math]\vec{r}=1m \hat{r}+\pi rad \frac{m}{rad} \hat{\theta}[/math]

>>8132129
>>8132123
is that what you're saying? if so why? is it defined this way?

>>8132129
>>8132131
The technical answer is that we treat angles as unitless because problems arise from, for example, attempting to carry radian "units" through trigonometric functions. However, in your simpler case, I find it fairly logical to write it similar to how you did and find that radians cancel leaving a sum of meters, and hope that maybe that helps your intuition a bit.

>>8132143
So if i calculate the norm of it, I'll end up with
[math]\left| \vec{r} \right|=\sqrt {r^2 +\theta^2}[/math]
which is intuitively wrong? i dont even know if this word exists, but shouldnt the norm be the radius?

>>8132079
kek'd audibly

>>8132151
The norm of that 1m.

>>8132219
but how do i get this result with some formalism?

>>8132220
Since you are using polar coordinates the norm is defined as the modulus of the term in [math]r[/math]

>>8132234
So is that thing about taking the square root of the dot product of the vector with itself is only valid in rectangular coordinates? How does dot product work in polar coordinates? Any source on that? thanks in advance

>>8132238
It's 6 a.m. here I'm drunk and I can barely read, I only dropped by to tell you the norm of a an euclidean vector in polar form is by definition what I said in my previous post.

>>8129288
http://www.ittc.ku.edu/~jstiles/220/handouts/The%20Position%20Vector.pdf

>>8132309
thank you so much thats all i needed, love you anon /thread

>>8129353
polar coordinates are fine, theyre just not vectors.