Questions tagged [question-verification]
This tag is for checking the validity of a question or a problem
28
questions
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Let $X$ be a set with $n$ elements. Prove that $ \sum_{Y, Z \subseteq X}|Y \cap Z|=n \cdot 4^{n-1} $
Let $X$ be a set with $n$ elements. Prove that $$
\sum_{Y, Z \subseteq X}|Y \cap Z|=n \cdot 4^{n-1}
$$
The sum is over all possible pairs $(Y, Z)$ of subsets of $X$.
I do not need a solution, but ...
0
votes
0
answers
53
views
"General" vs "Galois" Triple Plane
Suggested solution from comments: The curves $R$ and $R_0$ in the definition of "general" triple planes are usually assumed to be different.
I am currently working in the following setting: ...
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0
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A question in Strauss PDE exercise 9.4.2
In chapter 9.4 of Strauss PDE, we try to find the solution of 3D Diffusion Equation. And there is a exercise which is closely relating to the proof, as following:
$$\lim_{t\to0} \iiint_{R^3} S_3(X-X',...
- 41
1
vote
1
answer
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Circuit Probability Question from Mathematical Statistics
From Mathematical Statistics, 7th ed., Chapter 2, Supplementary Exercise no. 2.163:
Relays used in the construction of electric circuits function properly with probability $0.9$.
Assuming that the ...
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1
vote
1
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At most A does not occur
Let $A$ and $B$ be two events in the sample space $S$. Describe & represent the following event in terms of $A$ and $B$: "at most $A$ does not occur".
This is a question that someone ...
- 5,254
0
votes
2
answers
52
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Null sets cannot be covered by intervals for sufficiently small $\epsilon$ [closed]
I was trying the prove the following statement (Folland 1.5.30):
If $E\in\mathcal{L}$ and $m(E)\gt0$, for any $\alpha\lt1$ there is an open interval $I$ s.t. $m(E\cap I)\gt\alpha m(I)$.
The easiest ...
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2
votes
0
answers
61
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Extension of C1 functions
I studying the extension problem for classes of function $C^0,C^1,D^1$ ($D^1=$class of derivable function).
For $C^0$ function there is Tietze theorem and for $D^1$ function there is Jarnik theorem (...
- 382
6
votes
1
answer
101
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How do I check if this number is transcendental?
Two days ago, I tried to create an infinite series that might be able to generate a transcendental number, and when I checked the proper definition, it was mentioned that, it is a number that cannot ...
- 73
1
vote
1
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Calculating the area enclosed by three graphs, but two out of them already enclose a different area.
I have three functions :
$$y = 2x^2 + 2x \tag{1}$$
$$y = -x - 1 \tag{2}$$
$$x = 0 \tag{3}$$
Exercise asks for the area enclosed by three of those functions.
It is clear that the area from $x = \frac{-...
- 13
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Two variable functions and continuity
Since
$$\lim_{(x,y)\to(0,0)}\frac{x^4-y^4}{x^2+y^2}=\lim_{(x,y)\to(0,0)}\frac{(x^2+y^2)(x^2-y^2)}{x^2+y^2}=\lim_{(x,y)\to(0,0)}(x^2+y^2)=0$$
and
$$\lim_{(x,y)\to(0,0)}\frac{x^4}{x^2+y^2}=\lim_{(x,y)\...
- 2,124
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votes
2
answers
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Are these test paper questions as unclear and ambiguous as I think they are?
The Local Education Authority here in Wales are running a free voluntary course online for maths dunces like me to help us to help our 7-14 year olds with maths.
There's a free optional paper leading ...
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52
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What does c mean in the following question on cardinality?
I found a question in Modern Real Analysis by William P. Ziemer. The question can be found in Section 2.1 Question 1. It goes:
Use the fact that $\mathbb N =$ {$ n: n = 2k$ for some $k \in \mathbb N$} ...
- 377
3
votes
2
answers
210
views
If $x^2+bx+a=0, x^2+ax+b=0$ do not have distinct real roots then find the maximum value of $\frac{a^2+b^2}{a+b}$ if $a,b\gt0$
If $x^2+bx+a=0, x^2+ax+b=0$ do not have distinct real roots then find the maximum value of $\frac{a^2+b^2}{a+b}$ if $a,b\gt0$
Solution:
$D\le0\implies b^2-4a\le0, a^2-4b\le0$
It implies $b^2+a^2\le4(...
- 8,388
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votes
3
answers
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Something's not right about my understanding about identity matrices.
I tried the following problem.
Let $A = \begin{bmatrix} \alpha & 0 \\ 0 & \beta \end{bmatrix}$ and $B = \begin{bmatrix} 0 & \gamma \\ \delta & 0 \end{bmatrix}$.
There are 2 statements:
...
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0
answers
38
views
Max number of emails processable by consumer of email server
I saw this statement awhile ago, and I'm bit confused about how it works.
Suppose you have an email server that can only receive 3 emails every minute, and additional emails are filtered out. (Aside: ...
- 413
1
vote
1
answer
199
views
Finding the equation of a circular cylinder
I need to find the equation of the circular cylinder whose generators are parallel to the line $x=y=z$ whose guiding curve is the circle:
$$x^2+y^2+z^2-2x-3=0, \ \ 2x+y+2z=0 $$
My approach I assumed ...
- 1,239
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33
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Compound statement for a simple graph
Below I want to show a property of a simple graph $G=(V,E)$ - a graph in which each edge connects two different vertices and where no two edges connect the same pair of vertices - using a compound ...
2
votes
0
answers
71
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Solution check and question clarification request about a question on "generalized monoid" in Category theory.
The following question is taken from Arrows, Structures and Functors the categorical imperative by Arbib and Manes
In chapter 7 of Arbib and Manes about Functors. The authors introduce the category ...
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1
vote
1
answer
61
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(How) can two words differ in fewer places than the minimum distance?
I'm working on an unassessed course problem (which I paraphrase for conciseness),
Let $C$ be the code over $\mathbb{F}_5$ with generator and parity-check matrices
$$G=\begin{pmatrix}2&3&4&...
- 2,281
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votes
0
answers
21
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Finding distinct value that makes up the Integer partition under multiple constraints.
I'm working on a problem that want me to solve for solutions given four equations that is equal to an integer,
For instance, consider the variables $a_1,a_2,\dots,a_m\in \mathbb{Z}_{\geq 0}$ $a_n\neq ...
- 1,081
3
votes
2
answers
129
views
Understanding a question in combinatorics
I need help to understand a question in combinatorics.
One corner square in a $3 \times 3$ grid is painted black, the other
squares are white. In one move you can change color in all squares in
a row ...
- 2,985
1
vote
0
answers
29
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Finding a polynomial of order h from the first h+1 terms
In class we were finding a quadratic series from the first couple terms, I found that the equation of a quadratic sequence p1, p2, p3 is (p1-2p2+p3)x^2/2 +(-5p1+8p2-3p3)x/2 +3p1-3p2+1p3 but I want to ...
- 17
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38
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Is the variance of a random variable related to difference of square factorization?
Let $X$ be a random variable. The variance ($\sigma_X^2$) of $X$ is calculated by the formula:
$$\sigma_X^2=\Bbb E[X^2]-(\Bbb E[X])^2$$
Is there two operators acting on $X$ that outputs $\sqrt{\Bbb E[...
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vote
1
answer
58
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Constructing a parallelepiped with all faces having equal diagonals, what goes wrong?
I'm trying to construct a parallelepiped where each face has diagonal lengths $d_1$ and $d_2$. I start by constructing a parallelogram in the $x,y$ -plane that has the correct diagonals. I put that it ...
- 10.2k
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1
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Is the existence of a linear operator between two vectors always possible? [closed]
I have some questions to gain insigth on some core concepts of linear algebra:
Supose $V(\mathbb{C}^n)$ is a complex vector space, $\{v,u\}\in V$ are arbitrary distinct vectors with $v≠0$. Can we ...
-2
votes
1
answer
59
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I dont understand this problem [closed]
How is the answer to this not -6? Please solve this without U substitution because I need to know what I did wrong to get a negative answer. I did interval (B) - (A) as you should
$$\int_{-21}^0 \...
- 11
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vote
1
answer
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$M_1^2+M_2^2+M^2_3=M$ ,where $M_1,M_2,M_3$ are positive numbers and sum of any two is greater than the third, show that $2M ≤ (M_1 +M_2 +M_3)^2 ≤ 3M.$
$M_1^2+M_2^2+M^2_3=M$ ,where $M_1,M_2,M_3$ are positive numbers and sum of any two is greater than the third, show that $2M ≤ (M_1 + M_2 + M_3)^2 ≤ 3M.$
My solution goes like this:
We know that, $M_1^...
- 2,620
0
votes
2
answers
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views
If $2\cos\alpha_1=a+ \frac1a$ ,$2\cos\alpha_2 =b+ \frac1 b$ , etc... then show that $abc +\frac{ 1}{ abc} + ... = 2 \cos(\alpha_1 + \alpha_2 + ...)$
If $2\cos\alpha_1=a+\frac1a$,$2\cos\alpha_2 =b+\frac1b$, etc... then show that $abc +\frac{1}{abc} + ... = 2 \cos(\alpha_1 + \alpha_2 + ...)$
I don't get how to solve this problem. I tried the ...
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