/sqt/: Stupid Questions Thread

If it's not an equation with complex eigenvalues you shouldn't really need to find a diagonalized matrix... And even if you were to diagonalize it it would not require a rotation matrix.
This has a pretty obvious first solution, being Ce^(-t), and to find a second solution you need to find a generalized eigenvalue of that matrix- namely a value of lambda such that
[math]
(A-\lambda I)^2 = 0
[/math]

abstain ftw

sorry, determinant of that.

Abstaining works better because I can't stop masturbating if I start.

lel same

that's why i have to study at the library

Library doesn't work for me. I always end up figuring out a way to masturbate.

lel. i get distracted by qties

Same. I can't get myself to go to the library instead of masturbating.

Yeah the solution to this one is pretty easy. Just fixing up my notes, and would like an easy worked example.

[eqn] x = c_1 \exp (-t) + c_2 t \exp (-t) [/eqn]

I might have the signs wrong

Would you say you are addicted?

Yes.

Is it true that the geocentric model isn't exactly wrong, it simply leads to complicated math and retarded revolutions of the planets around the earth?

It's fucking wrong because gravity, nigga
Nothing intrinsic about the theory matters.

He just multiplied the top and bottom of the fraction by 2, and distributed the negative sign into the e^x terms.

Wow, great explanation, "nigger."

Black people should be banned.

>Implying I'm black
Models that don't accurately predict things thay they try to model are wrong. That simple. The trick is to know when the model's wrong or not.

The heliocentric model isn't quite right either. The Earth orbits the barycenter of the Sun-Earth system, which isn't always within the Sun.

You can construct the terran-centric model, but it's a non-inertial frame.

You're non-inertial, boyo.

Yes, you can construct a geocentric model that predicts the same observations a heliocentric model does. However it'd not be capable of explaining why the planets move that way, since it's complicated motions cannot be explained with gravitation or any know physical law.

First day on Veeky Forums?

What are some useful tools or techniques to figure out how matric multiplication will affect vectors?
It's a total pain to calculate one possible vector at a time; can I make some sort of 3D map of vectors, rendered based on how the matrix would affect those vectors?

My problem is that when a vertex of an object passes off-camera, my maths causes that vertex to fuck off some random place which of course makes a total mess of rendering.

That gives me a basic understanding, but it doesn't let me understand why things happen like a vertex suddenly jumping to another place.

What's the difference between undergraduate and graduate school? In terms of content, material and grading on what?

Is there something like Gilbert Strang's series of recorded lectures about linear algebra, but for discrete math?

There's this: ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/
But these are actual classroom lectures as opposed to Strang's style

Looks interesting, thanks. I will miss Strang and his savant ability to explain various concepts and how they interact.

How are most of you formatting equations? Word? LateX?

undergraduate: emphasis on coursework
graduate: emphasis on research

...

Can someone explain to me why this proof of the rational numbers between 0 and 1 has Lebesgue measure 1 is wrong? I know it is wrong as the converse is true, but the proof itself seems pretty satisfactory.

Suppose that the rational numbers between 0 and 1 have Lebesgue measure e such that e < 1. Then there exists a countably infinite sequence S of open intervals S such that the union of every set in S contains every rational between 0 and 1 and has measure e, which is less than any other possible union of open intervals that still contains all of the rationals between 0 and 1. We assume that the sets in S are disjoint; if not, an alternative sequence S' could be created such that for all n, S'n = Sn set minus the union of all of the intersections between Sn and the S'ms such that m < n; each set in S' would have less than or equal measure to its counterpart in S, so this sequence would have lower Lebesgue measure than S, which would contradict S's claim to have the least total length of any covering of the rational numbers between 0 and 1. We can therefore re-index S with indexing T such that for all j, the endpoint of Tj is less than the start points of all Tk such that k > j. Denote the endpoints of the various sets in T as a11, a12, a21, a22, a31, ... So S = T = (a11, a12) U (a21, a22) U (a31, a 32) U ..., with the endpoints of these intervals being of increasing order.

Now, take N = (0, 1) / T. This is clearly equal to (0, a11] U [a12, a21] , still with countably many intervals. As (0, 1) is of measure 1 and T is of measure e, N must be of measure 1 - e, which is greater than 0 as e < 1. So at least one of the intervals in N must have Lebesgue measure > 0; take that interval, note that since it's an interval it contains all numbers between its start and endpoint, produce a rational from density, and you obtain a contradiction.

I abused notation here a little with S and T standing either for a sequence of intervals or a union, but you get the gist.

>which isn't always within the Sun

How far out does it get?

>S'n = Sn set minus the union of all of the intersections between Sn and the S'ms such that m < n

An open set minus an open set is not necessarily open.

Thanks for this; this blows up my proof quite handily and allows me a greater intuition as to why the converse is true; the problem is that the sets are non-disjoint.

So I'm working on a problem, and I have an approximate solution from a slightly different problem which I'm working through for understanding before I get to work on my own one as I'm somewhat rusty on the math.

Basically I understand everything up to this point, where I get

[eqn]
S = 2 \epsilon_0 \epsilon_r \sum_{n=1\ (odd)}^{\infty} A_n (\frac{n\pi}{a}) cos \frac{n\pi x}{a} cosh \frac{n\pi b}{2a}
[/eqn]

Now, I also have as an approximation the condition that
[eqn]
S(x) = 1 \ for\ |x|\frac{W}{2}
[/eqn]

Next the author says, "Equating these and using the orthogonality properties of the cos(n pi x/a) functions gives the constants An such that:"

[eqn]
A_n = \frac{2a\ sin\frac{n \pi W}{2a}}{(n \pi)^2 \epsilon_0 \epsilon_r cosh \frac{n \pi b}{2a}}
[/eqn]

And it's this step that loses me. I have no idea what it means for the cos term to be orthogonal (and thus magically turn into a sin?), nor how the overall jump was made from S=... to An=... . Does anybody know how the math would go in this? Or have something similar I can look at to see how it works so I can figure this one out? It's probably something quite simple but I've been at the overall problem for a while now and I'm just totally stumped.

Actually, wait a second; can't you induct upwards from S using the triangle inequality in such a way that each generation of a given element of S's sequence is either equal to the union of the corresponding element from the previous generation and all other elements that were not disjoint with it, or the null set if last generation's corresponding element was already pulled into some other element this generation? Because you've only got countably many sets, eventually you'll run out of non-disjoint sets and the process terminates, and it's a valid thing to do because the triangle inequality exists so each generation will have less than or equal measure to the last generation. So you'd still have gaps in the line that the complement can come in and screw you over with thanks to density.

I dunno but this might help: (scrolling down a bit) tutorial.math.lamar.edu/Classes/DE/PeriodicOrthogonal.aspx

Can you said that a vectorial space is a sub-vectorial space of itself or is it retarded ?

Yes, just like a set is a subset of itself. It's not retarded, but it's trivial. (also, in english it's a vector space not a vectorial space you silly frenchman)

Ahh that's actually quite helpful, thanks a lot!

Why is psychological addiction a thing?

youtube.com/watch?v=36GT2zI8lVA

Bumpity

...

Is there a mathematical model to predict the center of orbit on a flat plane from just those recorded points?

What if it's a set of all sets that don't include themselves?

That's not a set :^)

Where the hell is the ∉ key?

Sure it is. Let's call it R (like bertrand Russell).
R = { x | x ∉ x}

How is that not a set?

>How is that not a set?

Before we proceed, let's define "set." You first.

That's pretty straightforward. It's a collection of objects. In this case, it doesn't really matter if it's a collection of mathematical objects, and a set itself is also an object.

Are we really gonna go down the rabbit hole and ask each other to explain set theory from the ground up?

>Are we really gonna go down the rabbit hole and ask each other to explain set theory from the ground up?

Yes, because the resolution to Russell's paradox is that you cannot construct the set of all sets that do not contain themselves from the axioms of ZFC. Also, "set" is undefined, like "point" and "line" in Euclid :^)

how would you prove the riemann hypothesis? if it's false, it would suffice to provide a single example of a non-trivial zero with a non-0.5 real part, right? but if it's true, what kind of proof would be needed?

i mean that's literally the million dollar question... but there ought to be some previous work/ideas on this subject to read about

Hehe that was fun

Let z be a zero of the Riemann Zeta function. (some equations or whatever) Therefore Re(z) = 1/2.

Alternatively, assume Re(z) is not 1/2. (some equations)
(a contradiction)

You're right about the false part.

Yeah. Check out the 2-body problem

Yes, providing a number that breaks the hypothesis would be sufficient. But that's not the only way to prove it's false; lots of disproofs of theorems are given without actually providing a counterexample (the first example of this I encountered in number theory is that pi(x) > Li(x) infinitely often, which was proven but didn't give an actual number, and it was 20 years before anybody even got a bound on where that number was)

Describing "what kind of proof" is needed in concrete terms is impossible. There's a decent probability it may not even be a direct proof of the original statement because there are six bajillion statements equivalent to the Riemann Hypothesis nowadays.
Nobody is close enough to doing it (as far as I know) to say with any heft that their approach is the right one. And even when (if) somebody finally does it the proof is likely going to be absurdly technical and inexplainable to anyone who isn't an expert in the particular subfield it came from.

I think I really fucked up...

How strict are colleges about deadlines? I just realised that a few of my college choices require a Math II subject test, which I never took. They sat scores are all due January 1st...will my application be canceled or can I still take the january sat subject test?

You may be fucked. Big administrations don't like making exceptions for people, especially when your excuse for needing the exception is either "I forgot" or "I didn't read the requirements".

That said they do want your money so you _may_ be able to arrange something, although don't count on it. Call the offices of the colleges you're looking at immediately and try to find somebody in admissions who can help you or confirm you're screwed.

any organic chemistry people here? taking org 1 and there's this one stupid question about diels alder reactions having two adducts that I can't get right for the life of me. It's this online homework site OWL, doesn't give great advice on the specifics you are getting wrong.

Hey Veeky Forums, I'm approaching the limit of transferable courses I can take at my community college. My problem is that I don't really care for getting my degree just yet, and would personally rather burn through my FAFSA taking all the classes I find interesting. I've yet to dabble into chemistry and philosophy at my community college, but doing so would put me well over the transferable limit, meaning some classes were essentially for nothing (though they also were free through FAFSA).

Anyone have any recommendations here? Should I just suck it up and move on to a four year, or should chill and enjoy life and soak up that dank free knowledge?

Why does one whiff of pic related get me instantly high? Most inhalants, you have to huff for ten or twenty seconds to get anywhere.

>"set" is undefined

Thank GOD someone speaks the truth. I get so fucking triggered whenever one of my profs defines a set.

I don't know if I'm saying bs but maybe it is because Lebesgues' mesure of the sets containing the rationnal numbers in [0;1] is not the same as Lebesgues' mesure of the set of rationnal numbers in [0;1]

Can you spell that out more clearly? I don't know what you're trying to say.

Actually, the problem I pointed out can probably be fixed (using closed intervals is essentially the same) -- an interval minus a finite set of intervals is always a finite set of intervals. So, I'm not sure what the real problem is. I'm skeptical that finding a smaller disjoint cover is possible.

cool, thanks

That's only one possible resolution. The set of all sets that don't contain themselves DOES exist in NF. It uses stratified formulas instead of building up the set universe iteratively.

Wildmemer pls go

Wait, never mind. It doesn't exist in NF either but for different reasons.

Could someone give a good sample of TeX notations so I can right-click it and see the code? I'd like to see all the fundamentals so I can pick it up and use it quickly.

Y'know, fractions, abs, Boolean operators and equal sign variants, integrals (including contour and surface), matrices, vector notations, summations, pi product notations, probabilistic and set functions, subscripts, roots, derivative notations, unique symbols like the Laplace transform and the set of reals, size controls, and color palettes.

sharelatex.com/learn

i have to write a script that computes the pearson correlation of two signals of different lengths using the conv function in matlab
im being told that if i do conv(x,fliplr(y)) that ill get the cross correlation, but when i do that i get pic
left being regular correlation and right being the conv thing
im very confused
any help much appreciated

I need some real advice in how to prepare for the EJU exam.
These are the syllabi:
www.jasso.go.jp/sp/en/eju/examinee/syllabus/index.html
(I only need

I would appreciate any (books, pages, study plan, schedule, whatever) recommendation!

I'm self studying and I'm free 24/7.

Sorry for asking this here, I don't know if it's the correct place to do so. If so, could you point me towards where I can ask this? (in my country there are no preparation courses decent enough)

[MATH] Euclidean division

n^5 + 5n^3 + 7n^2 + 8n + 19 = (n+7)q + r with 0

What to do when you're too intelligent to have friends and interact with females?

Why can you not create a 100% pure solution of ethanol by distilling a mixture of ethanol and water? I get that water and ethanol form an azeotrope at 95.6% which has a lower boiling point than the individual components.
However, if you start, say, with a 50:50 mixture of water and ethanol, as the ethanol evaporates, you will never reach a 95.6% concentration in your heated flask.

You can create a ethanol solution that is very close to pure. Something around 99%. Chances are there will be some water that comes along for the ride.

If [math]4^x + 4^{-x} = 34[/math], what is

[math]2^x + 2^{-x}[/math].
Any help? The answer is supposed to be 6.

You're not too intelligent, you're just setting your expectations too high for others. You should learn to conceal your intelligence and blend in with people. This in itself is an interesting challenge to a certain degree.

Square the second expression.

[eqn]4^x+4^{-x}=2^{2x}+2^{-2x}=(2^x+2^{-x})^2-2=34[/eqn]

Thank you very much.

divide the long polynomial by n+7 using the division algorithm

or

write q = an^4+bn^3+cn^2+dn+e and match the coefficients

I have a function that outputs a binary value. Is this notation valid?

[math]f: R \mapsto \{0, 1\}[/math]?

>autosaging
It's called a bump limit... Faggot

Also what if a function outputs a value between 0 and 1? Can I [math]f:R \mapsto [0, 1][/math]?

Yes
Yes

go into cocoon mode

focus on things you can do on your own that will help you become successful in life (building wealth, learning skills, improving your appearance etc)

You mean too unintelligent

please tell me that complex numbers aren't the final frontier of algebra

please

they're not

so, is there any operation that needs a new kind of number?
or are you referring to abstract infinite aleph shit?