# Search results

1. ### What is the field with one element ?

What is the "field with one element"? From the definition of a field, it follows that such a thing does not exist. However a Google search reveals that apparently there is, or at least mathematicians think there ought to be, something that goes by that name. What is it? Is it called a "field"...
2. ### Integration using Partial Fractions

I suppose you can use \int\frac{a}{b\pm x}dx=\pm a\ln|x\pm b| - Kamataat
3. ### Integral of 2/(y+1)?

Remember that dx=d(x+c), c=const. - Kamataat
4. ### Simultaneous equations help

For the first one, the answer (\log_q2=p/4) is OK, but I have trouble understanding what you wrote before that. For the second one, you can't assume that 16=8q. Otherwise, you're on the right track: \log_q(8q)=\log_q8+\log_qq=3\log_q2+1 You already know what \log_q2 is in terms of p, so...
5. ### Infinite number of open intervals

OK, I apologize for this mess. Feel free to delete that posting of mine. More careful next time. - Kamataat
6. ### Infinite number of open intervals

A union of sets is composed exactly of the elements of those sets (no more, no less). Let's say we have the sets A=(a,b) and B=(c,d), where a<b<c<d. If their union were closed, then it would have to a) include "more" elements than there are in A and B, for example their endpoints OR b) include...
7. ### Induction question

Prove by induction that 2^{2^n}+1 always ends in 7 for all n > 1 (true for n = 2). I couldn't figure out anything to do with the last digit being 7, so I looked the case that 2^{2^n} ends in 6 for all n > 1, which is also true for n = 2. Suppose it's true for n = k: 2^{2^{k+1}}=2^{2^k\cdot...
8. ### Definition of the Definite Integral

I think s/he means \lim_{\max\Delta x_k\rightarrow 0}~sum=L - Kamataat
9. ### What is a T-line and a N-line

Never heard of those terms, but if T-line is the tangent then N-line is the normal line (the line perpendicular to the tangent at x=-4) I suppose. - Kamataat
10. ### Gravitational Force and Field

FS is vector directed away from the origin of the field. The magnitude of a resultant vector can be smaller that the magnitudes of the vectors being added. - Kamataat
11. ### Gravitational Force and Field

You sure you calculated correctly? For the sun I get F=G\times\frac{M_{sun}}{(\frac{r}{2})^2}=6,672\cdot 10^{-11}\times\frac{7,67\cdot 10^{30}}{(\frac{2,72\cdot 10^{11}}{2})^2}=2,767\cdot 10^{-2}\frac{N}{kg} - Kamataat
12. ### Gravitational Force and Field

Calculate the sun's grav. field magnitude at r/2 and then the planet's at r/2. Add these to get the total. - Kamataat
13. ### Pot. energy

Thank you! - Kamataat
14. ### Pot. energy

So if a question asks to find the speed which a body must achieve at ground level to escape the Earth's grav. field, then I can take E_p@infinty = 0? From that |E_k|=|E_p| to find the speed? - Kamataat
15. ### Pot. energy

If h, the height of a body from the ground, approaches infinity, then the body's potential energy approaches 0? I'm assuming a non-constant value for g. E_p = mgh. In this equation I get 0 times infinity, which is mathematically indeterminate, but I'm guessing that the physical interpretation...
16. ### PF is taken over by space robots?

OK, I'll give this a chance, but it IS irritating for the eyes. Maybe another "calm" skin in the future (yeah, I know, it's hard work)? - Kamataat
17. ### Quick question

Still having trouble with this. Here's what I know: Anti-symmetric: Definition 1: xRy \wedge yRx \Rightarrow x=y Definition 2 (equivalent to #1): x\neq y \Rightarrow \rceil(xRy) \vee \rceil(yRx). I have the set {a,b}. The cross-product {a,b}x{a,b}={(a,a),(a,b),(b,a),(b,b)} and a relation on...
18. ### Quick question

Grrrr, there's a typo in my original post. I meant antisymmetric not asymmetric. Sorry. edit: My lecturers textbook has this written in it: "... {a,a,b,c} and {{a,b},{b,a}} do not denote sets, because the elements of a set are distinct." I have read about multiplicity the way you write about...
19. ### Quick question

The antisymmetric relations on a set {a,b} are those, which do not contain both of the pairs (a,b) and (b,a) because that would imply a = b, however a can't equal b since they are elements of a set? PS: In our course we allow only one copy of an element in a set, so {a,b} is a set only if a...
20. ### How can I find the radius of this circle?

Divide AD in two with a point E. Now from the triangle OAE you get OA=AE/cos(62). Draw the bisector of AD from O to the line AT, call the point it makes on line AT point F. The projection of AF onto AD is AE, from this we get AF=AE/cos(28)=2,55 cm, which is not equal to TA and thus OT does not...
21. ### Mixed questions [Functions and Sequenzes & Series]

The function is strictly decreasing for x < -3. - Kamataat
22. ### Mixed questions [Functions and Sequenzes & Series]

For #2, what condition must a function meet for an inverse to exist? Does g meet this condition for x <= -3? edit: sign error - Kamataat
23. ### Sin/cos inverse - derivitives

Use {y'}_x = \frac{1}{{x'}_y}. Take y=\arcsin x and x=\sin y. - Kamataat
24. ### A proof of relations

Yeah, especially since it's such an elementary thing. I'd think anyone with a (future) professional interest in maths/physics should know this stuff like the back of his/her hand! Oh well, it's happened before to me, so... /rant Anyway, thanks! - Kamataat
25. ### A proof of relations

I answered this wrong on a test, but now I've come up with a different solution. Problem: Prove that a relation xRy\Leftrightarrow x-y\in\mathbb{Z} defined on \mathbb{R} is an equivalence relation. Solution: 1.) Reflexivity: xRx,\forall x\in\mathbb{R} For every x we have x-x=0 which is an...
26. ### Mechanics-related car question

The acceleration is wrong. You need to use the same units for all variables. - Kamataat
27. ### Is it possible to work out the centre of an ellipse?

Look at this: http://mathworld.wolfram.com/EccentricAngle.html - Kamataat
28. ### Is it possible to work out the centre of an ellipse?

But the ellipse IS centered at the origin. It asks for the eccentric angle between the x-axis and the line joining (0,0) and (2,1). edit: PS: The eccentric angle is not simply arctan(y/x), you have to take the axes of the ellipse into account too! - Kamataat
29. ### Function proof

So if any element of f(X\A) were also in f(A), then that element must have two originals, one in A and one in X\A, and hence the function is not injective? - Kamataat
30. ### Function proof

I had this question on a test today. Prove that if a function f:X-->Y is injective, then f(X\setminus A) \subset Y\setminus f(A), \forall A \subset X. This is how I did it: If x_1 is in A, then y_1=f(x_1) is in f(A). Because the function is injective, we can pick (cut Y into pieces) f(A) and...