User Vincent

9 votes

5 answers

7k views

If $\mathcal{P}(A)=\mathcal{P}(B)$, then $A=B$? [duplicate]

asked Mar 15, 2014 at 19:47

9 votes

3 answers

4k views

Teaching the Concept of Infinity to Children.

asked Aug 7, 2014 at 2:35

7 votes

2 answers

2k views

If $f$ is continuous on $[a,b)$ and $[b,c]$, then $f$ is Riemann integrable on $[a,c]$.

asked Dec 12, 2014 at 21:22

7 votes

5 answers

5k views

Probability event with $70$% success rate occurs three consecutive times for sample size $n$

asked Jan 4, 2017 at 6:41

5 votes

1 answer

971 views

Proving Archimedes Sequences Equal $\pi$.

asked Sep 19, 2014 at 7:59

4 votes

5 answers

10k views

If a connected graph has a unique spanning tree, then it is a tree.

asked May 11, 2014 at 0:59

4 votes

2 answers

889 views

Checking Initial Values of an IVP

asked May 15, 2014 at 8:16

4 votes

3 answers

2k views

Probability a 9-digit number has the digits 2,4, and 6 next to each other.

asked Jun 16, 2014 at 22:44

4 votes

4 answers

2k views

How to integrate: $\int_{0}^{\infty}e^{tx}(x^2e^{-x})/2dx$

asked Jun 21, 2014 at 0:39

4 votes

3 answers

2k views

Interesting Mathematical Fallacies [duplicate]

asked Jun 27, 2014 at 7:29

3 votes

1 answer

152 views

Given a family $\mathfrak{F}$ for sets, when are $\bigcup \mathfrak{F}$ and $\bigcap \mathfrak{F}$ empty?

asked Mar 15, 2014 at 1:14

3 votes

2 answers

3k views

Traditional combination problem with married couples buying seats to a concert.

asked Jun 17, 2014 at 9:21

3 votes

2 answers

752 views

If $f$ takes $[-1,1]$ onto $[-1,1]$ then $f^{-1}(\{f(0)\})=\{0\}$

asked Sep 5, 2014 at 5:58

3 votes

1 answer

175 views

Evaluating $\int_{0}^{2}\sqrt{x^3+1} dx+\int_{1}^{3}\sqrt[3]{x^2-1}dx$ without computation?

asked Dec 10, 2014 at 11:02

2 votes

1 answer

98 views

Variation of Fermat's Theorem

asked Sep 10, 2014 at 12:05

2 votes

1 answer

432 views

Proving $\{x_n\}$ converges to $a$ when $|x_n-a|\le Cb_n$ for large $n$ and $C$ is a positive constant.

asked Sep 12, 2014 at 7:19

2 votes

2 answers

166 views

Proving if $a$ and $b$ are positive rational numbers and $\mathbb Q(\sqrt{a})=\mathbb Q(\sqrt{b})$ then $b=ac^2$ for some $c\in \mathbb Q$.

asked Oct 4, 2014 at 7:16

2 votes

2 answers

532 views

How to prove the $\lim\limits_{x\to 1} \frac{1}{\log x}$ does not exist.

asked Oct 1, 2014 at 1:00

2 votes

4 answers

802 views

Finding the cube roots of $-i$.

asked Oct 4, 2014 at 2:58

2 votes

1 answer

311 views

Prove by induction that $\sum_{i=0}^n \left(\frac 3 2 \right)^i = 2\left(\frac 3 2 \right)^{n+1} -2$

asked Mar 15, 2014 at 0:27

2 votes

1 answer

61 views

Is this proof by induction correct?

asked May 10, 2014 at 23:17

2 votes

1 answer

9k views

Finding a pdf from a CDF with a Discrete Random Variable

asked Jul 16, 2014 at 9:56

2 votes

5 answers

3k views

A machine has $9$ switches. Each switch has $3$ positions. How many different settings are possible?

asked Jun 17, 2014 at 0:38

2 votes

2 answers

3k views

How many words can be formed from 'alpha'?

asked Jun 11, 2014 at 4:52

1 vote

3 answers

246 views

Prove: $\sum_{x=0}^{n} (-1)^x {n \choose x} = 0$

asked Jun 13, 2014 at 4:48

1 vote

1 answer

1k views

$P(A \cup B) = 1 - P (A' \cap B')$

asked Jun 5, 2014 at 3:52

1 vote

2 answers

8k views

Let $f(x,y)=cx(1-y), 0<x<2y<1$, and $0$ otherwise. Find $c$. Are $x$ and $y$ independent?

asked Jul 16, 2014 at 13:19

1 vote

1 answer

185 views

Is it possible to create a bigger square using distinct smaller ones?

asked Jul 23, 2014 at 7:01

1 vote

1 answer

72 views

Finding Probabilities of Distribution Functions

asked Jun 23, 2014 at 4:41

1 vote

2 answers

3k views

Finding the probability an equation has real roots.

asked Jun 27, 2014 at 1:42

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74 Questions

If $\mathcal{P}(A)=\mathcal{P}(B)$, then $A=B$? [duplicate]

Teaching the Concept of Infinity to Children.

If $f$ is continuous on $[a,b)$ and $[b,c]$, then $f$ is Riemann integrable on $[a,c]$.

Probability event with $70$% success rate occurs three consecutive times for sample size $n$

Proving Archimedes Sequences Equal $\pi$.

If a connected graph has a unique spanning tree, then it is a tree.

Checking Initial Values of an IVP

Probability a 9-digit number has the digits 2,4, and 6 next to each other.

How to integrate: $\int_{0}^{\infty}e^{tx}(x^2e^{-x})/2dx$

Interesting Mathematical Fallacies [duplicate]

Given a family $\mathfrak{F}$ for sets, when are $\bigcup \mathfrak{F}$ and $\bigcap \mathfrak{F}$ empty?

Traditional combination problem with married couples buying seats to a concert.

If $f$ takes $[-1,1]$ onto $[-1,1]$ then $f^{-1}(\{f(0)\})=\{0\}$

Evaluating $\int_{0}^{2}\sqrt{x^3+1} dx+\int_{1}^{3}\sqrt[3]{x^2-1}dx$ without computation?

Variation of Fermat's Theorem

Proving $\{x_n\}$ converges to $a$ when $|x_n-a|\le Cb_n$ for large $n$ and $C$ is a positive constant.

Proving if $a$ and $b$ are positive rational numbers and $\mathbb Q(\sqrt{a})=\mathbb Q(\sqrt{b})$ then $b=ac^2$ for some $c\in \mathbb Q$.

How to prove the $\lim\limits_{x\to 1} \frac{1}{\log x}$ does not exist.

Finding the cube roots of $-i$.

Prove by induction that $\sum_{i=0}^n \left(\frac 3 2 \right)^i = 2\left(\frac 3 2 \right)^{n+1} -2$

Is this proof by induction correct?

Finding a pdf from a CDF with a Discrete Random Variable

A machine has $9$ switches. Each switch has $3$ positions. How many different settings are possible?

How many words can be formed from 'alpha'?

Prove: $\sum_{x=0}^{n} (-1)^x {n \choose x} = 0$

$P(A \cup B) = 1 - P (A' \cap B')$

Let $f(x,y)=cx(1-y), 0<x<2y<1$, and $0$ otherwise. Find $c$. Are $x$ and $y$ independent?

Is it possible to create a bigger square using distinct smaller ones?

Finding Probabilities of Distribution Functions

Finding the probability an equation has real roots.