tchappy ha's user avatar
tchappy ha's user avatar
tchappy ha's user avatar
tchappy ha
  • Member for 7 years, 5 months
  • Last seen more than a month ago
  • Tokyo
23 votes
3 answers
1k views

Is a characteristic polynomial we consider in Linear Algebra a polynomial or a polynomial function?

9 votes
2 answers
1k views

Exercise 6.A.17 in "Linear Algebra Done Right 3rd Edition" by Sheldon Axler. I am worried if my solution is ok.

8 votes
3 answers
514 views

Is it true that if $\limsup\limits_{n \to \infty}\left|\frac{a_{n+1}}{a_n}\right| > 1$, then $\sum a_n$ diverges?

7 votes
1 answer
932 views

A simple question about the proof of theorem 3.42 in Walter Rudin's "Principles of Mathematical Analysis"

7 votes
2 answers
2k views

Is there a simple abelian group $G$ with infinite order?

7 votes
1 answer
1k views

I heard that tensors are a generalization of scalars, vectors, and matrices. But tensors don't look like matrices at all.

6 votes
3 answers
5k views

A group with 4 elements

6 votes
1 answer
121 views

A proof of Eisenstein's criterion and a related proposition in "Lectures on Algebra" by Teiji Takagi.

6 votes
1 answer
143 views

The author defined $0\cdot\infty=\infty\cdot 0=0$. Why is this convention good. ("Measure, Integration & Real Analysis" by Sheldon Axler.)

6 votes
1 answer
108 views

What is the value of $\frac{1}{2}\int_B\int_B\frac{\rho(x,y,z)\rho(x',y',z')}{4\pi\epsilon_0\sqrt{(x-x')^2+(y-y')^2+(z-z')^2}}dxdydzdx'dy'dz'$?

5 votes
1 answer
127 views

Is there a very small gap or no gap in this proof? ("Linear Algebra Done Right 3rd Edition" by Sheldon Axler.)

5 votes
1 answer
199 views

Is the notion of indefinite integrals really necessary in analysis? (Walter Rudin "Principles of Mathematical Analysis 3rd Edition")

5 votes
2 answers
491 views

How many solutions are there for the equation $a^x = \log_a x$, where $0 < a < 1$?

5 votes
1 answer
89 views

Why is $T: C^\infty(\mathbb{R}) \ni f \mapsto (a_n) = (f^{(n)}(0)) \in \mathbb{R}^\mathbb{N}$ surjective?

5 votes
2 answers
265 views

About a lemma to prove the Cantor-Bernstein-Schroeder theorem.

5 votes
1 answer
301 views

The definition of the set of positive integers in "Topology 2nd Edition" by James R. Munkres.

5 votes
1 answer
107 views

Is $\emptyset$ a finite union-closed family of finite sets, other than the family containing only the empty set or not

4 votes
1 answer
66 views

About the axioms of a metric space. I think we don't need (D2) to show (D1).

4 votes
0 answers
41 views

$f:X\to Y$ and $g:Y\to X$ are bijective and continuous. Then two metric spaces $X$ and $Y$ are homeomorphic? [duplicate]

4 votes
1 answer
180 views

The collection $\{x : \exists y(x\in y)\}$ is not a set. ("Set Theory: A First Course" by Daniel W. Cunningham)

4 votes
1 answer
77 views

Can we compose two empty mappings?

4 votes
0 answers
78 views

Prove $\psi^n=-1$ ("The Design and Analysis of Computer Algorithms" by Aho, Hopcroft, Ullman)

4 votes
1 answer
149 views

A theorem about absolutely convergent series. Please tell me a rigorous proof.

4 votes
3 answers
178 views

I can understand this $B$ is symmetric. But I cannot understand why $B$ is positive definite.

4 votes
1 answer
192 views

Why did Spivak choose this definitions? ("Calculus on Manifolds", the definition of the norm, the definition of open sets)

4 votes
1 answer
122 views

About $\log (1 + x)$ on p.427 "Calculus 4th Edtion" by Michael Spivak

4 votes
0 answers
495 views

About Theorem 5.13 in "Principles of Mathematical Analysis" by Walter Rudin L'Hospital's Rule L'Hopital's Rule

4 votes
3 answers
133 views

About $e^{i z} = \cos z + i \sin z$ in Michael Spivak "Calculus 3rd Edition".

4 votes
2 answers
584 views

Does this proof that every open set in a metric space is a union of open balls use the axiom of choice?

4 votes
1 answer
529 views

About a proof of Cayley-Hamilton theorem in "Linear Algebra" by Ichiro Satake.

1
2 3 4 5
18