Counterexample of $X_{n}$ and $Y_{n}$ converging in $L^{1}$ but not their product
119638
convergence in $L^1$ for product of functions
78654
An example of a norm which can't be generated by an inner product
4672
Example of two convergent series whose product is not convergent.
63344
Why is $\underbrace {i^{i^{i^{.^{.^{.^{i}}}}}}}_{n \ times}$ converging?
129087
Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
101701
Prove that $\ln x$ is not uniformly continuous on $(0,1]$
54952
Is it true that $\limsup\sqrt[n]{|a_n|}=\limsup\sqrt[n]{|a_n-a_{n-1}|}$, ($n>1$), where $\{a_n\}$ does not have a finite limit?
18125
Counterexamples to the converse to Lagrange's Theorem different from $A_{4}$.
33050
proof that translation of a function converges to function in $L^1$
132701
Contradicting Fubini's theorem
131425
Prove that the convergence of $\prod_{n=1}^{\infty} b_n$ implies $\lim_{n→∞} b_n = 1$
118903
The sup norm on $C[0,1]$ is not equivalent to another one, induced by some inner product
63418
Show that $f_n(x) = \frac{x^2}{n}$ for $x \in \mathbb{R}$ does not converge uniformly towards $0$ for $n \rightarrow \infty$
17779
Proving the Limit of a Sequence of without the Dominated Convergence Theorem
7078
If $\sum_n \sqrt{a_n a_{n+1}}$ converges, then $\sum_n a_n$ might not converge.
57014
Existence of a power series converging non-uniformly to a continuous function
65888
A counterexample to theorem about orthogonal projection