Examples and counterexamples
Some facts can be seen more clearly by example than by proof.
If I were wrong, one would be enough.
Einstein’s reply to hearing of the Nazi book 100 Authors Against Einstein
Now we come to one of the biggest secrets in thinking like a mathematician. So far in this book we have covered many of the important tools for logical thinking: statements, implications, quantifiers. Many other books cover these. But they cover in little detail what I consider to be one of the most important tools. It is ...