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Results tagged with counterexamples
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user 21724
A counterexample is an example that disproves a mathematical conjecture or a purported theorem. For example, the Peterson graph is a counterexample to many seemingly plausible conjectures in Graph Theory.
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The $n$-th derivative has $n$ zeros. Can such a function be unbounded?
As suggested by Mateusz Kwaśnicki, the function $f : x \mapsto (1+x^2)^{s}$ is bell-shaped and unbounded for any $s \in (0,\frac{1}{2})$.
It is easy to see that $f^{(n)}(x) = P_n(x) (1+x^2)^{s-n}$ wh …
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