Consider the following (obviously) wrong proposition:
Proposition:
All positive natural numbers are definable in under eleven words.
Proof:
Suppose for the sake of contradiction(!) that not all positive natural numbers are definable in under eleven words. Then there is a smallest integer n∈N which is not definable in under eleven words. But this number is
"the smallest positive integer not definable in under eleven words",
therefore, it is definable in ten words. Contradiction!
Wat je wiskunde al niet allemaal kan doen
