Questions tagged [solution-verification]
For posts looking for feedback or verification of a proposed solution. "Is this proof correct?" or "where is the mistake?" is too broad or missing context. Instead, the question must identify precisely which step in the proof is in doubt, and why so. This should not be the only tag for a question, and should not be used to circumvent site policies regarding duplication.
65 questions from the last 30 days
7
votes
2
answers
1k
views
Why does this method work some of the time (but only some?)
This question showed up in an exam for 11-year olds:
Alice bought some chocolate and vanilla muffins. $\frac{3}{4}$ of her muffins are chocolate and the rest are vanilla. She then bought another 60 ...
- 850
3
votes
5
answers
525
views
How many elements are present in the subset of a null set?
Consider :
How many elements are present in the subset of a null set?
This is one of the question that appeared in my math exam.
Definition $1.1$ - Subset:
A set $A$ is a subset of set $B$ if all ...
- 47
4
votes
6
answers
231
views
Proving $ \angle MAN = 45^\circ$ in an isosceles right triangle
Regional Mathematical Olympiad 2003 (India)
Let $ABC$ be a triangle in which $AB =AC$ and $\angle CAB = 90^{\circ}$. Suppose that $M$ and $N$ are points on the hypotenuse $BC$ such that $BM^2 + CN^2 = ...
- 3,478
1
vote
4
answers
196
views
Find the $n^{th}$ derivative of $f(x)=\frac{x}{x^{2}+a^{2}}$ [closed]
I need clarity in finding out the $n^{th}$ Derivative of $$f(x)=\frac{x}{x^{2}+a^{2}}$$
My Thought
Let's Assume $x=a\tan\theta$
$$\implies f(x)=\frac{a\tan\theta}{a^{2}\sec^{2}\theta}$$
$$\implies f(x)...
- 1,836
5
votes
6
answers
312
views
Show that $x^2+y^2-2ixy$ is not an analytic polynomial.
To show that $x^2+y^2-2ixy$ is not an analytic polynomial. We assume that it is an analytic polynomial and try to reach a contradiction. First we write
$$x^2+y^2-2ixy=\sum_{k=0}^N \alpha_k(x+iy)^k.$$
...
7
votes
2
answers
351
views
Proving that the set of the quotients of Fibonacci numbers is not dense in the positive reals
As in the heading, I'm trying to write up a proof that the quotients of all Fibonacci numbers is not dense in $\mathbb{R_+}$. This is what I have come up with and would like to know if it's correct.
...
- 85
2
votes
3
answers
184
views
How to solve $ \lim\limits_{x\to+\infty} \!\!\left(\! \frac{x^{2}+3}{3x^{2}+1}\! \right)^{\!x^{2}}\!\!\!=0\;?$
I know it can be solved with Squeeze's theorem, but I want to verify that this more conventional method might also be valid.
$$ \lim_{x\to+\infty} \left(\frac{1+\frac{3}{x^{2}}}{1+\frac{1}{3x^{2}}}\...
- 23
2
votes
2
answers
125
views
Is the isomorphism $(G/N_1)/(N_2/N_1)\cong G/N_2$ in the third isomorphism theorem actually an equality?
I tried to understand the concept that, for a group $G$ and two normal subgroups $N_1,N_2$ with $N_1\subseteq N_2$ it holds that
$$(G/N_1)/(N_2/N_1)\cong G/N_2,$$
but my following reasoning seems to ...
5
votes
1
answer
189
views
Arrangements of 10 Balls Chosen from Red and Blue, Where Every Blue Ball Has a Blue Neighbor(need pure combinatorics solution)
Question
Consider a linear arrangement of $10$ balls selected from an infinite supply of blue and red balls.
Determine the total number of distinct arrangements that satisfy the following condition:
...
1
vote
3
answers
303
views
Rigorous proof that $f(x) = 0$ for all $x$
This question appeared in an objective test:
Let $f(x)$ be a continous and integrable, nonpositive function defined on $[0,\infty)$ such that $F(x) = \int_0^x f(x)dx$, and $\exists c \in \Bbb R^+$ ...
- 5,861
2
votes
2
answers
97
views
The least positive integer ending in $7$ which quintuples if the $7$ is moved to the front
I wrote up an attempt at the first problem in "Problem Primer for Olympiad," which is:
Find the least number whose last digit is $7$ and which becomes $5$ times larger when this last digit ...
7
votes
1
answer
188
views
Polynomial $p(x) \in\mathbb Z[x]$ such that $n\nmid p(0), p(p(0)), p(p(p(0))), \dots$.
So the following question is from a recent but concluded contest.
Question: Let $p(x)$ be a nonconstant polynomial with integer coefficients such that there exists $n\geq 2$ such that none of the ...
- 5,631
2
votes
2
answers
222
views
Proving every two composition series of a module are of the same length (half of the *Jordan-Holder theorem*)
This is a second followup question to this question I asked a couple of days ago (here is the first followup question). After resolving the issues I raised in both of the linked questions I proceeded ...
- 205
-6
votes
1
answer
102
views
Is this proof for infinitude of primes valid? [closed]
A Simple Pattern-Based Proof of the Infinitude of Prime Numbers
Note:
I’m a student developing a simple logical version of the proof that prime numbers are infinite.
I would appreciate comments on ...
0
votes
4
answers
154
views
The quadratic equation $x^2 - (c+3)x + 9 = 0$ has real roots $x_1$ and $x_2$. If $x_1 < -2$ and $x_2 < -2$, find value of $c$.
The quadratic equation $x^2 - (c+3)x + 9 = 0$ has real roots $x_1$ and $x_2$. If
$x_1 < -2$ and $x_2 < -2$, then the value of $c$ is ...
I try:
Since there are two real root then
\begin{align}
...
- 2,988