Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [question-verification]

This tag is for checking the validity of a question or a problem

This tag is used for checking the validity of a question. It is used when a user is confused about whether the problem encountered is at all legit or not. The user typically uses this tag if one encounters some anomaly in the problem and wants the community to verify the question or problem as the case may be. In short, this is a verification tag.

32 questions
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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: $AB - BA$ is always an invertible matrix, and $AB - BA$ is…
Harikrishnan M
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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 be expressed as a root of any non zero polynomial…
Teflon
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3
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2 answers

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 $b^2+a^2\le4(a+b)\implies \frac{b^2+a^2}{a+b}\le4$ So, the…
aarbee
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3
votes
2 answers

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 or in a column. Can you get all the squares…
Superunknown
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2
votes
1 answer

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 rather I need help in understanding this problem,…
OlympiadRunner
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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 (rediscovered by G. Petruska and…
user791759
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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: It's not clear to me if every minute is disjoint…
roulette01
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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 of generalised monoid as motivation and precursor…
Seth
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1
vote
2 answers

2015 IMOSL Problem Statement Interpretation

IMOSL 2015 C1 ( available here ) In Lineland there are $n$ towns, arranged along a road running from left to right. Each town has a left bulldozer (put to the left of the town and facing left) and a right bulldozer (put to the right of the town and…
Illusioner_
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vote
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You have a sheet one centimeter thick you can create sheets half as thick as the previous one if you put one on top an infinite number where it finish

I am 13 years old and this question came to my mind during recess. And I think I have an answer but I would like your approval. -The question: If I have a 10-meter-high ceiling and a 1cm thick sheet of paper; if you have the possibility (in an ideal…
Kevin Pedone
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How to prove that solutions of semilinear differential equations is even function?

My question comes from the book Stable Solutions of Elliptic Partial Differential Equations Louis Dupaigne, pages 30-32. Summary: Which uniqueness theorem to use for this differential equation ? I am working with the following semilinear…
Richard
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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: $$\lim_{t\to0} \iiint_{R^3} S_3(X-X',t)\phi(X')~dX'=\phi(X)\tag{6}$$ Prove that (6)…
郭冠廷
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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 circuits operate independently, which of the…
Mailbox
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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 asked me, and I think it is meaningless as "at most" makes no…
Fermat
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1 answer

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 $x = \frac{-1}{2}$ to $x = 0$ is included, but the problem is…
lptd
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