Hello everyone,
I've been struggling quite a bit with this problem, since I'm not sure how to approach it correctly. The inequality form reminds me of the equation of a circle (x^2 + y^2 = r^2), but I have no idea how to be sure about it. Would it help just to simplify the inequality in terms...
Summary: Given three points on a positive definite quadratic line, I need to prove that the middle point is never higher than at least one of the other two.
I am struggling to write a proof down for something. It's obvious when looking at it graphically, but I don't know how to write the...
Hi, I am studying a paper by Yann Bugeaud:
http://irma.math.unistra.fr/~bugeaud/travaux/ConfMumbaidef.pdf
on page 13 there is an inequality (16) as given below-
which is obtained from -
, on page 12.
How the inequality (16) is derived? I couldn't figure it out. However one of my...
Hi all,
I was wondering if there exist any theorems that allow one to relate any joint distribution to its marginals in the form of an inequality, whether or not ##X,Y## are independent. For example, is it possible to make a general statement like this?
$$f_{XY}(x,y) \geq f_X (x) f_Y(y)$$...
Homework Statement
I would like to know how the boundary of the inequality change when the origin of the coordinate system changes.
Homework Equations
The original inequality is[/B]
$$ r_0 \le x^2+y^2+z^2 \le R^2$$
I would like to know the boundary of the following term, considering the...
I was browsing through Spivak's Calculus book and found in a problem a very simple way to prove the cauchy schwarz inequality.
Basically he tells to substitute x=xᵢ/[√(x₁²+x₂²)] and similarly for y (i=1 and 2), put into x^2 + y^2 >= 2xy. Add the two cases and we get the result.
The problem is...
Hi, I found in Kreyszig that if for any ##x_1\ and\ x_2\ \in \mathscr{D}(T)##
then an injective operator gives:
##x_1 \ne x_2 \rightarrow Tx_1 \ne Tx_2 ##
and
##x_1 = x_2 \rightarrow Tx_1 = Tx_2 ##
If one has an operator T, is there an inequality or equality one can deduce from this...
problem statement:
need to show:
||w||_p^2+||u||_p^2-2(||u||_p^p)^{\frac{2}{p}-1}\Sigma_i(u(i)^{p-1}w(i))
can be bounded as a function of
||w-u||_p^2
where p\in[2,\infty)
work done:
the expressions are equal for p=2, and i suspect that...
Hi there,
I'm having trouble understanding this math problem:
|x| + |x-2| = 2
The answer says its: 0<=x<=2
I understand you need different "cases" in order to solve this. For example, cases for when x is less than 0, when x-2 is less than 0, etc.
Thanks,
blueblast
The Bell Inequality tests are only valid for positive numbers, which is reasonable because counts and probabilities cannot be negative. CHSH generates a negative number, which means CHSH experiments are invalid.
Bell's Inequality can be violated by having a negative value.
For example...
Hi.
I wonder if following thought experiment (which is most probably impossible to be put into practice) could have any implications concerning interpretations of QM.
Consider five parties A, B, C, D and E, lined up in that order and with no relevant relative motion. No pair of them have ever...
Homework Statement
If a,b,c,d,e>1
then prove that
a^2/(c-1)+b^2/(d-1)+c^2/(e-1)+d^2/(a-1)+e^2/(b-1)=>20
The Attempt at a Solution
Given a,b,c,d,e are roots of a polynomial equation of a degree 5 then
x^2/(x-1)+x^2/(x-1)+x^2/(x-1)+x^2/(x-1)+x^2/(x-1)=>20
5 x^2/(x-1)=>20
x^2/(x-1)=>4...
Homework Statement
$$
\left | \frac{z}{\left | z \right |} + \frac{w}{\left | w \right |} \right |\left ( \left | z \right | +\left | w \right | \right )\leq 2\left | z+w \right |
$$
Where z and w are complex numbers not equal to zero.
2.$$\frac{z}{\left | z \right | ^{2}}=\frac{1}{\bar{z}}$$...
Homework Statement
If a,b,c are positive real numbers such that ##{loga}/(b-c) = {logb}/(c-a)={logc}/(a-b)## then prove that
(a) ##a^{b+c} + b^{c+a} + c^{a+b} >= 3##
(b) ##a^a + b^b + c^c >=3##
Homework Equations
A.M ##>=## G.M
The Attempt at a Solution
Using the above inequation, I am able...
Homework Statement
##|4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x| > 8*6^x(8^{x-1}+6^x)##
For some numbers ##a, b, c, d## such that ##-\infty < a <b < c <d < +\infty ## the real solution set to the given inequality is of the form ##(-\infty, a] \cup [b, c] \cup [d, +\infty)## Prove it by arriving at...
[b[1. Homework Statement [/b]
##|4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x| \ge 8*6^x(8^{x-1}+6^x)##
The sets containing the real solutions for some numbers ##a, b, c, d,## such that ##-\infty < a < b < c < d < +\infty## is of the form ##(-\infty, a] \cup [b, c] \cup [d, +\infty)##. Prove it by...
Homework Statement
Using the principle of mathematical induction, prove that for all n>=10, 2^n>n^3
Homework Equations
2^(n+1) = 2(2^n)
(n+1)^3 = n^3 + 3n^2 + 3n +1
The Attempt at a Solution
i) (Base case) Statement is true for n=10
ii)(inductive step) Suppose 2^n > n^3 for some integer >=...
Hello all,
I want to prove the following inequality.
sin(x)<x for all x>0.
Now I figured that I put a function f(x)=x-sin(x), and show that it is increasing for all x>0. But this alone doesn't prove it. I need to show we have inequality from the start. I can't show that lim f(x) as x->0 is...
I'm interested in the following inequality (which may or may not be true)
Theorem 1:
##( \sum_{i=1}^n \frac{a_i} {n}\ )( \sum_{i=1}^n \frac{1} {b_i}\ ) > \sum_{i=1}^n \frac{a_i} {b_i}\ ##
Where ##n ≥ 2, a_1 < a_2 < ... < a_n## and ##b_1 < b_2 < ... < b_n##.
My attempt at a proof:
1) When n =...
Homework Statement
$$x+\frac{16}{\sqrt{x}} \geq 12$$
How do I show that only x>0 satisfies the inequality above.
Homework Equations
The Attempt at a Solution
I have not made a lot of progress here. I tried the following:
$$x+\frac{16}{\sqrt{x}} - 12 \geq 0$$
I tried to multiply with $$...
So I was helping my sister on homework and there was this problem:
2 abs(2x + 4) +1 > or equal to -3
teacher told her to ignore the -3 and just set it equal to zero.
Soo should you? This question got me confused. can't you just go about solving, bringing the 1 to the left and then dividing by 2...
Hi
I'm trying to solve this inequality
|1/(2+a)| < 1.
1/(2+a) < 1 ∨ 1/(2+a) > -1
1 < 2+a
a > -1
and
1 > -2-a
3 > -a
a > -3
I know that the boundaries are
-∞ < a < -3 ∨ -1 < a < ∞
What have I done wrong?
thanks in advance