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"...
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...
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...
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...
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
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
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
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
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...
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...
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...
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...
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...
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
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...
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
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
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...