## Welcome to Math Counterexamples!

I initiated this website because for years I have been passionated about Mathematics as a hobby and also by “strange objects”. Mathematical **counterexamples** combine both topics.

The first counterexample I was exposed with is the one of *an unbounded positive continuous function with a convergent integral*. I took time to find such a counterexample… but that was a positive experience to raise my interest in counterexamples.

According to Wikipedia *a counterexample is an exception to a proposed general rule or law. And in mathematics, it is (by a slight abuse) also sometimes used for examples illustrating the necessity of the full hypothesis of a theorem, by considering a case where a part of the hypothesis is not verified, and where one can show that the conclusion does not hold*.

By extension, I call a **counterexample** any example whose role is not that of illustrating a true theorem. For instance, a polynomial as an example of a continuous function is *not* a counterexample, but a polynomial as an example of a function that fails to be bounded or of a function that fails to be periodic *is* a counterexample.

While I’m particularly interested in Topology and Analysis, I will also try to cover Logic and Algebra counterexamples.

And obviously, I welcome any suggestion!

Jean-Pierre Merx

Paris – France

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