Wouldn't it depend on whether the points of the set belong to an open or closed (well, actually a compact) set? If it is closed it has definite end points but not if it is open.
Wouldn't it depend on whether the points of the set belong to an open or closed (well, actually a compact) set? If it is closed it has definite end points but not if it is open.
How do I find the derivative of x^(2/3)-x^(1/3)?
Power rule. d/dx[x^n] = nx^(n-1).
Apply to this. Your case is nothing special, n just isn't an integer.
Writing the Linear Algebra test next week (same as Swebonny I think).
Haven't studied enough.
Screwed... What's most disturbing is the fact that the course isn't that hard really. Gosh darn!
Oh hey I have a Linear Algebra test next week too
For algorithm analysis, how could I prove that
I can't use the limit rule as the function oscillates
If I have 2 numbers and if one of them is rational and the difference between them is rational as well, then the other number is rational, too, right? So, if I take any number and 1 which is a rational number and take the difference between the two and if that difference is rational, the second number is rational. Well, so we can test the difference for rationality the same way we did for the first number, infinitely. If we do this we eventually get a difference of 0, which is rational, so by backpedelling infinitely, we should get that all numbers in that chain are rational.
What is wrong in that reasoning?
Subtracting a finite number of terms from an infinite sum still gives you an infinite sum
Edited:
Wait, what? I don't think I'm understanding you.
Well, if I want to test 3 for rationality, I can find the average point between the two and the distance between that average point to 1 and 3. Since we assumed 1 is rational, if the distance from 1 and the average point is rational, then the A.P which is 2 is also rational. and since 2 is rational and the distance from 3 to is rational, then so is 3.
Well, if I want to test e this way, I have no guarantees that the first AP or the first distance are rational (but if one is true, then the other is true, too), but I can test the first ap this way, too, I just find the ap to the first ap, the second ap.
If I do this infinitely, the Aps will grow closer and closer to 1, the distance between them will be zero. Zero's a rational number, which means that the infinieth AP will be rational, so i can test our original number against this AP, the same shit'll happen and if I keep testing the original number against the APs infinitely, I'll eventually hit the original number which will be, therefore, rational.
But during no single actual test for e will come out rational. It only tends to a rational in the limit. That doesn't make e rational.
I don't think I understand how this works.
You have no guarantee that the first ap or distance is rational, but if you've subtracted a rational number from e then the difference is guaranteed to be irrational. The distance between the average point and the rational number is irrational because the average also is irrational.
Can someone tell me how to find the absolute value of a complex number?
In what I suggested? I didn't even mess with e or tried to gauge its worth. I mean, I'm not saying e's rational, I'm just saying I don't understand why my thought's wrong.
You're right, though. lim x -> infinity 1/x = 0, 1 and 0 being integers doesn't make infinity an integer.
And I believe it's sqrt (a^2 + b^2), the Pythagorean theorem applied to the coordinates.
Is it possible for a quintic function to have two real roots?
You can have only have two distinct real roots but not two real roots of multiplicity one, since you need an even amount of complex roots.
You can have something like: f(x)=(x-3)(x+i)(x-i)(x-2)^2=(x-3)(x^2+1)(x-2)^2 which has two distinct real roots.
Looks easy, but it really isn't. (It scared JohnnyMo1 into not talking to me still.)
You could say that the girl = x, the mom = 2x, and the boy = 4x (since the boy gets twice as much as the mom, the mom gets twice as much as the girl), and that totals 7x. Therefore you make it out in sevenths. Boy gets 4/7, mom gets 2/7, and girl gets 1/7.
But maybe I'm dumb. :(
It's kind of a dumb problem. Not really mathematics.
Okay, I've gotten it to graph z^z by setting the domain to -3.5<x<3.5 for the real and imaginary axes.
I'm guessing it has something to do with the precision of the applet.
Yeah, I think we're in the same school lol (KTH right?). Yeah it's not really that hard, the course book is great. Saying that I still got shit results, at least I passed it
Edited:
Time for Multivariable calculus now. Perhaps I will work harder.
Something I just noticed about the roots of one.
The square root of one is 1 or -1.
The fourth roots of one are 1,-1,i,-i.
The eighth roots are those previously listed along with both square roots of both positive and negative i.
It would follow that the infinite root of 1 would be a unit circle along the complex plane, and that 1^0 has infinitely many values, amongst them i. The principle value, of course, being one.
Furthermore, any number with an absolute value of x would then equal any point on that circle you take the last root.
Therefore, infinitesimals are baaad and I should stop using them.
Edited:
Q.E.D.
The square root of one isn't 1 and -1. It's just 1.
On the other hand, the solution to x^2 = 1 is x = 1 and x = -1.
Q.E.D
I've been doing a lot of Fourier Series/Transforms lately and I find them really interesting. Not very difficult, but they are so useful in real life applications.
Useful, sure. Fun? Hell naw. Fourier transforms are hella ugly.
The series are kinda cool though.
I'm doing it in the context of electrical engineering. So they are a lot more straight forward because they are all related to real life application. There just simply aren't that many possibilities.
I've been wanting to learn about how these work, but I haven't finished calculus yet, so I have no idea what's going on
I'm programming an app for locating wifi signals with a GPS.
The program associates a position vector with a signal strength. The position vector is normalized to a two-dimensional vector (expressed in meters) and the signal strength is normalized to watts.
From my understanding of physics it seems that the signal strength is inversely proportional to the square of the distance. Meaning that for any arbitrary position v, the power is approximately
where x is the location of the source of the signal and k is some constant.
Or equivalently:
Measuring the signal strengths P(v) at multiple different positions v gives me an overdetermined system of polynomial equations (of the second degree).
But I haven't the faintest idea how to solve x out of them.
Can't you do some kind of substitution?
It's just an infinite (theoretically) amount of orthogonal functions that are multiplied by some constant and then added together. With this sum you can create literally any periodic function. It's pretty awesome.
I just came here to say that Logarithms are THE SHIT and they're the best thing to happen to math ever.
Hey, I am currently in an engineering program and I am having trouble with the math. Specifically getting good at integrals. I have tried learning them from khan academy but they don't seem to help much with the types of problems we get. Is there any really good resource for learning integrals from the very basics to more advanced because i have a month to study before my exam and am really freaking out.
Try :
http://ocw.mit.edu/courses/mathemati...ideo-lectures/
Really good videos. I've been watching the multi-variable calculus lectures. God damn I love the lecturer, our is rather bad. .
Hey guys I have a couple of resources/tools might be relevant to your interests.
http://graph.tk/ is a pretty fast and simple HTML based graph utility.
And then there's this.
http://douweosinga.com/projects/arch...m=random+value
I remember having that kind of trouble in the beginning with epsilon delta stuff. I just expected it to be something it wasn't.
Can someone explain what a "perfect differential" is? It came up in mechanics to show a force is conservative, and my lecturer skipped over it entirely. He wouldn't test it, it's just out of interest's sake. And if it is not immediately obvious from its definition, how would this show a force is conservative if fdr is a perfect differential?
what would be the quickest way of inverting a 5 by 5 matrix by hand?
the only method i know (for a 3 by 3) involves calculating the determinants of a bunch of 2 by 2s using its elements, but scaling that up to 5 by 5, that'd be like what, 3600 determinants of 2 by 2 matrices or something?
which would just be silly
Edited:
also please tell me if that statement was just outright dumb, because it's late and i can't ~maths~
I haven't heard it called a perfect differential, but I assume it means that it is path independent. (because of the conservative nature)
Yeah, I know it would have to imply that but i doubt it's defined as that.
Two really stupid questions inbound.
Let's say I have a wave pair of arbitrary periodic waves. I draw these inside a modeling program on the sides of a long box running along the positive end of the program's Z axis, and use those to generate one of...these.
First question, what do you call the third (black) wave? Like, what type of wave is it when it's along more than two axes? I only ever dealt with them regarding light polarization before, I don't know the mathematical term.
Anyway, the second question, the real question, is this. Let's say I disable the visibility of the waves on the sides of the box, and leave only the third, black one visible. So, if I'm viewing this box along its Z axis, rotated along the Z axis to see the box only along its X and Z axes, I see the third wave in the shape of the wave drawn on that side of the box. If I rotate it along the Z axis to view only the Y and Z axes, I see the other. But if I view it by some arbitrary rotation about the box's Z axis, I see other two axis waves, which change with the rotation.
How do you define those waves in terms of the two waveforms they are drawn from and the Z axis rotation they are viewed from?
I'm pretty sure that'd be a torsional wave, I imagine you could describe a particle on that wave in cylindrical co-ordinates (and if you wanted convert back to Cartesian). You'd have constant radius, and i think from the other two waves you could figure out its height and a rotation from the origin of theta.
If you were building it out of two sine waves with same speed, angular velocity etc, I'm pretty sure if you're interested about a point on the wave, if it's at height z=k it would stay on that plane, move on a circle with constant radius, with the radius given by the amplitude of one of the 2D waves you're using to describe it, and angle from the point (0,0,k) changing at a constant rate (I think it'd change with the same angluar velocity as the waves). If you wanted to image that wave propagating through space, you'd have a changing z which moves at the same speed as the 2D ones. Then again I've never done waves like this in my life so I might be wrong, this is just what I imagine would happen.