mathcounterexamples.net

Paris, France

http://www.linkedin.com/in/jpmerx

I'm living in Paris, France and doing Math as a hobby, with special interest in Mathematical logic and Analysis.

I opened in July 2014 a website dedicated to Math Counterexamples. I welcome any suggestion for additional counterexamples... at least at a level that I can understand!

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Results true in a dimension and false for higher dimensions

big-list counterexamples vector-spaces asked Sep 14, 2014 at 16:44

mathoverflow.net

36 votes

Why does this sequence converges to $\pi$?

nt.number-theory sequences-and-series asked Jan 14, 2015 at 17:54

mathoverflow.net

30 votes

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

abstract-algebra group-theory asked Jun 28, 2015 at 1:42

math.stackexchange.com

18 votes

What are your favorite instructional counterexamples on sequences?

calculus examples sequences asked Feb 1, 2015 at 9:39

matheducators.stackexchange.com

16 votes

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

sequences-and-series asked Sep 13, 2015 at 13:35

math.stackexchange.com

14 votes

ODE properties true in finite dimension but not in Banach spaces of infinite dimension

differential-equations banach-spaces counterexamples asked Jan 11, 2015 at 10:56

mathoverflow.net

13 votes

Well ordering agreeing with ordinal ordering on a cardinal

set-theory order-theory asked Jun 18, 2015 at 20:47

math.stackexchange.com

13 votes

Right English wording for "counterexamples to a theorem"

terminology examples-counterexamples asked Aug 31, 2015 at 11:50

math.stackexchange.com

12 votes

Listing methods to prove that two groups are not isomorphic

group-theory big-list group-isomorphism asked Jun 17, 2018 at 10:04

math.stackexchange.com

11 votes

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

calculus real-analysis notation asked Dec 9, 2015 at 22:11

math.stackexchange.com

Top Answers

Proof: Is there a line in the xy plane that goes through only rational coordinates?

math.stackexchange.com

Proof that the number of proofs is countably infinite

math.stackexchange.com

Is $F=\left\lbrace f: f\in C_{\left[0, 1\right]}, f\left(0\right)=f\left(1\right)\right\rbrace$ complete metric space?

math.stackexchange.com

$ \bigcup_{n=1}^{\infty}\{z\in\Bbb C:z^n=1\}=\{z\in\Bbb C:|z|=1\}$?

math.stackexchange.com

Convergence of infinite sum (factorial and root)

math.stackexchange.com

How to check if a function is convex

math.stackexchange.com

Differentiability of a two variable function $f(x,y)=\dfrac{1}{1+x-y}$

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can polynomial functions with rational coefficients approximate any continuous function on $[a,b]$.

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A+B is closed if one of them is compact

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L'Hôpital's rule: number of iterations...

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Find $\lim\limits_{x\to \infty} \frac{x\sin x}{1+x^2}$

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Do the polynomials $(1+z/n)^n$ converge compactly to $e^z$ on $\mathbb{C}$?

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Computing $(1+\cos \alpha +i\sin \alpha )^{100}$

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Having difficulty understanding what happens when reversing order of quaternion multiplication.

math.stackexchange.com

Is this group of matrices cyclic?

math.stackexchange.com

Find the value $\int_{0}^{1}f(x) \,\mathrm dx$ without words

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Calculating limit of definite integral

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Prove that if $f$ differentiable in $x^*$ and $f(x^*)=0$, then $\liminf_{x\to x^*}\frac{|f(x)|}{||x-x^*||}=0$ if $n>1$

math.stackexchange.com

Let $f:[0,1]\to\mathbb{R}$ be a continuous function. Calculate $\lim\limits_{c\to 0^+} \int_{ca}^{cb}\frac{f(x)}{x}\,dx$

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Galois Group does not depend on the choice of the field extension

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Counterexample regarding basic properties of limits

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Sufficient condition for a matrix to be diagonalizable and similar matrices

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Why are inner products defined to be linear in the first argument only?

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Is the function defined by $f(x+1)=f(x)+f(1), f(2)=1$ just $f(x)=\frac{x}{2}$?

math.stackexchange.com

Are these formal formulas equivalent?

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Question about a subset

math.stackexchange.com

If $\lim\limits_{n\to +\infty}x_n=+\infty$ then $\left(\frac{x_n}{x_{n+1}}\right)_{n\in\mathbb{N}}$ converges

math.stackexchange.com

Is it necessary that two vectors will always be coplanar?

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Zeros of Polynomials in Arbitrary Rings

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What axiom of ZFC implies that "sets have no repeated elements"?

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