Carview!

-2 votes

0 answers

45 views

Proof for a question in the textbook "How to Prove It" by Daniel J. Velleman [duplicate]

Here's a question in the textbook: Let U be any set. Prove that there is a unique A ∈ P(U) such that for every B ∈ P(U), A ∪ B = B. The proof I made on my own goes like this: Let A equal the null set, ...

Nick

7

asked 6 hours ago

0 votes

0 answers

55 views

Show that a finitely generated group has only a finite number of subgroups of a given finite index (Hatcher page 87, exercise 8)) [closed]

This is a question from the exercise of Hatcher's Algebraic Topology. It asks to show that a finitely generated group has only a finite number of subgroups of a given finite index. My Attempt: As per ...

Dwaipayan Sharma

670

asked 17 hours ago

0 votes

0 answers

45 views

Proof and supplementary information for inequality problems

Problem: Let $a_1, a_2, \cdots, a_n$ be positive real numbers such that at most one of them is less than $1$ and $a_{1}^{3}+a_{2}^{3}+ \cdots +a_{n}^{3}=n$. Prove that $ a_1+a_2+ \cdots +a_n \le a_{...

user1274233

867

asked 20 hours ago

-1 votes

0 answers

59 views

How can I prove by induction that $\sqrt{1+\sqrt{2+\sqrt{\cdots +\sqrt{n}}}}<3$ for all $n\geq 1$? [duplicate]

I am trying to prove by the principle of induction that for every positive integer $n$ $$\sqrt{1+\sqrt{2+\sqrt{\cdots +\sqrt{n}}}}<3.$$ I have tried the following, although I am not sure where to ...

Guillemus Callelus

1,063

asked yesterday

0 votes

3 answers

64 views

Confusion in the statement of a theorem

I was watching this lecture on algorithms in graph theory. At time $11.53$, the narrator states a little theorem which I find confusing. I find this statement quite confusing and my argument is as ...

RAHUL

1,610

asked yesterday

0 votes

0 answers

54 views

Finding the smallest cube that contains a set of points?

I have $m$ points in $n$-dimensional space: Point 1: $(x_1^{(1)}, x_2^{(1)}, \ldots, x_n^{(1)})$ Point 2: $(x_1^{(2)}, x_2^{(2)}, \ldots, x_n^{(2)})$ $\vdots$ Point $m$: $(x_1^{(m)}, x_2^{(m)}, \...

stats_noob

4,155

asked yesterday

-2 votes

0 answers

43 views

Is there any mathematical flaw in this proof by induction on cardinalities? [closed]

Is there any flaw in the following proof by induction? Define set $B_{n}=\{b_{1},b_{2},b_{3},\cdots ,b_{n}\}$. For a particular even number $N\geq 8$, we define $b_{i}=N-p_{i}$, for $1\leq i\leq n$ ...

De Niz

1

asked yesterday

0 votes

2 answers

59 views

Countability of an Infinite Image of a Countable Set

This is a problem from the topology section of Bergman's Supplements to Rudin W. Principles of Mathematical Analysis. I was having some trouble with the hint provided and didn't understand how to ...

Need_Help

29

asked 2 days ago

6 votes

2 answers

174 views

Proving a subset of $\mathbb{Z}$ to be a subgroup of $(\mathbb{Z},+)$.

Let $G\subset \mathbb{Z}$ be a subset of integers which contains at least one positive integer and at least one negative integer. Suppose that $G$ is closed under the usual addition in $\mathbb{Z}$ i....

Sandeep Tiwari

772

asked 2 days ago

1 vote

1 answer

69 views

+50

Could these formula been accurate estimators of the Median Path of a Binomial Lattice Model?

Could these formula been accurate estimators of the Median Path of a Binomial Lattice Model? In the last added section I believe I almost show that the Expected Geometric Growth is actually the Median ...

Joako

2,035

asked Jul 28 at 3:07

1 vote

0 answers

29 views

Approximation in outer measure by an algebra

Let ${\mu_0: {\mathcal B}_0 \rightarrow [0,+\infty]}$ be a pre-measure on a Boolean algebra ${\mathcal B}_0$, and let ${\mu: {\mathcal B} \rightarrow [0,+\infty]}$ be the Hahn-Kolmogorov extension of $...

shark

1,573

asked Jul 27 at 22:12

0 votes

3 answers

94 views

Evaluating $\prod_{i=k}^{j-1}\frac{2i-1}{2i}$

Closely related to this question. Similarly to what was done in the answer to the question above, I would like estimate $$\prod_{i=k}^{j-1}\frac{2i-1}{2i}$$ I proceeded as follows: $$\prod_{i=k}^{j-1}...

Noam

453

asked Jul 27 at 15:21

4 votes

1 answer

105 views

Doubt on the regularity of a path in the proof of "Integral Invariance for Homotopic Paths"

I am studying a book of Complex Analysis called "Complex Analysis with Applications" by Asmar and Grafakos. I am confused about the regularity of a path in the proof of the following theorem....

Davide Masi

1,752

asked Jul 27 at 14:20

4 votes

1 answer

137 views

Show that solution of $f''(x)+p(x)f'(x)-\lambda f(x) = 0$ with $f(0)=f(1)=0$ is identically zero

Let $p(x), f(x)$ be two continuous functions on $[0,1]$ that satisfy: $$ f''(x)+p(x)f'(x)-\lambda f(x) = 0\quad \forall x \in (0,1). $$ If $\lambda > 0$ and $f(0)=f(1)=0$, is it true that $f=0 \...

연하준

159

asked Jul 27 at 6:42

4 votes

1 answer

104 views

Can you show $A \times \emptyset = \emptyset$ by showing that $|A \times \emptyset| = 0$?

I know in general that you can't say 2 sets are equal if they have the same cardinality. For example, let $A = \{1,2,3\}, B = \{a,b,c\}$. Even though, $|A|=|B|=3$, clearly $A \neq B$. The issue with ...

AeroMain27

293

asked Jul 26 at 21:33

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All Questions

Proof for a question in the textbook "How to Prove It" by Daniel J. Velleman [duplicate]

Show that a finitely generated group has only a finite number of subgroups of a given finite index (Hatcher page 87, exercise 8)) [closed]

Proof and supplementary information for inequality problems

How can I prove by induction that $\sqrt{1+\sqrt{2+\sqrt{\cdots +\sqrt{n}}}}<3$ for all $n\geq 1$? [duplicate]

Confusion in the statement of a theorem

Finding the smallest cube that contains a set of points?

Is there any mathematical flaw in this proof by induction on cardinalities? [closed]

Countability of an Infinite Image of a Countable Set

Proving a subset of $\mathbb{Z}$ to be a subgroup of $(\mathbb{Z},+)$.

Could these formula been accurate estimators of the Median Path of a Binomial Lattice Model?

Approximation in outer measure by an algebra

Evaluating $\prod_{i=k}^{j-1}\frac{2i-1}{2i}$

Doubt on the regularity of a path in the proof of "Integral Invariance for Homotopic Paths"

Show that solution of $f''(x)+p(x)f'(x)-\lambda f(x) = 0$ with $f(0)=f(1)=0$ is identically zero

Can you show $A \times \emptyset = \emptyset$ by showing that $|A \times \emptyset| = 0$?

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