Questions tagged [examples-counterexamples]
To be used for questions whose central topic is a request for examples where a mathematical property holds, or counterexamples where it does not hold. This tag should be used in conjunction with another tag to clearly specify the subject.
4 questions from the last 7 days
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Can there be a continuous function with infinite derivative everywhere?
Let $f:\mathbb{R}\to\mathbb{R}$ be continuous. For all nowhere-differentiable examples that I know of, for each $a\in\mathbb{R}$ there exist sequences $x_n\to a$ and $y_n\to a$ such that
$$\frac{f(...
- 9,329
0
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1
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Matrices that are related to their transpose via diagonalizable matrices
I'm currently working with matrices having the following property:
Let $A \in M_n(\mathbb Z)$ be square matrix such that there exist diagonalizable matrices $S,T \in M_n(\mathbb C)$ with $A = S A^t T$,...
- 197
2
votes
1
answer
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Counterexample for Unitary Operators and Orthogonal Complements
I'm working on an exercise of Friedberg's linear algebra book. In the previous parts of the exercise, I proved that if $U$ is a unitary linear operator on an inner product space $V$, and $W$ is a ...
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0
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Counter example to dominated convergence for nets
I came across the following counter example in the accepted answer to this questions A net version of dominated convergence?
For context, the original example is this:
Let $\Lambda$ be the set of ...
- 3,355