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mathcounterexamples.net
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30 votes
1 answer
3k views

Group $G$ whose center $Z(G)$ is cyclic and with $G/Z(G)$ commutative

12 votes
1 answer
965 views

Well ordering agreeing with ordinal ordering on a cardinal

12 votes
7 answers
2k views

Right English wording for "counterexamples to a theorem"

12 votes
3 answers
273 views

$a_n =0$ for all $n \in \mathbb N$ if $\sum a_n^k =0$ for all integers $k \ge 1$

10 votes
2 answers
206 views

Does $\infty$ mean $+\infty$ in "English mathematics"?

10 votes
4 answers
10k views

Listing methods to prove that two groups are not isomorphic

8 votes
1 answer
196 views

Probability measure on $\mathbb N$ such that $P(n \mathbb N) =1/n$ for all $n \ge 1$ cannot exist

7 votes
2 answers
213 views

For which matrices $A \in \mathscr{M}_n(\mathbb C)$ is the similarity class of $A$ closed?

7 votes
1 answer
284 views

A proof that Gaussian binomial coefficients are integers

7 votes
2 answers
1k views

Notation for the set of the subgroups of a group?

7 votes
2 answers
166 views

Defining the existence of a non algebraic element in the language $L:= \{0,1,+,\cdot\}$

7 votes
1 answer
200 views

Maximum number of commutators required to generate an element of the derived subgroup

6 votes
4 answers
191 views

If $(u_n)$ is bounded and $\lim u_n^2+u_n-u_{n+1}=0$ then $u_n \to 0$

6 votes
1 answer
118 views

For which $\mathcal{F} \subset C[0,1]$ does there exist a sequence converging pointwise to the supremum?

6 votes
1 answer
1k views

Counterexamples to Brouwer's fixed point theorem for the closed unit ball in Banach space

6 votes
5 answers
376 views

Computing as many digits as possible of $\sqrt{2}$ with a pen and a paper in 5 minutes

6 votes
1 answer
189 views

A linear map $\varphi$ such that $\varphi (GL_n(\mathbb C) )\subseteq GL_n(\mathbb C)$ preserves the rank

6 votes
2 answers
150 views

Is $\int_0^\infty \vert \sin x \vert^{x^2} \ dx$ convergent?

6 votes
2 answers
3k views

Is the quotient of a finitely generated module finitely generated?

5 votes
0 answers
96 views

Proving the existence of an integer $n$ such that $2^n=123456789...$ [duplicate]

5 votes
1 answer
1k views

Proving that $X^4+1$ is reducible over all finite prime fields

5 votes
2 answers
5k views

Examples of Separable Spaces that are not Second-Countable

5 votes
1 answer
732 views

Discontinuous bilinear form separately continuous

5 votes
1 answer
104 views

The solutions of $y^{\prime \prime}+y=g$ are bounded

5 votes
2 answers
227 views

English word for a "pavé" in French

5 votes
3 answers
614 views

Playing with closure and interior to get the maximum number of sets

4 votes
1 answer
142 views

Does $\lim\limits_{n \to +\infty} \left(\frac{n}{f(1)} \int_0^1 x^n f(x) dx \right)^n$ exists?

4 votes
3 answers
234 views

Asymptotic expansion at order 2 of $\int_0^1 \frac{x^n}{1+x} \, dx$

4 votes
1 answer
164 views

Asymptotic expansion of $f(x)= \sum_{n=1}^\infty \frac{\sin nx}{\sqrt{n}}$ at the origin

4 votes
3 answers
131 views

Functions satisfying the functional equation $ \big( 1 - f ( x ) f ( y ) \big) f ( x + y ) = f ( x ) + f ( y ) $