Introduction
The philosopher Wittgenstein didn’t like the set theory and complained mathematics is “ridden through and through with the pernicious idioms of set theory,” He dismissed the set theory as “utter nonsense”, as being “laughable” and “wrong”. His criticism appeared years after the death of the German mathematician Georg Cantor, the founder of the set theory.
Cantor defined a set at the beginning of his “Beiträge zur Begründung der transfiniten Mengenlehre”:
“A set is a gathering together into a whole of definite, distinct objects of our perception and of our thought – which are called elements of the set.” Nowadays, we can say in “plain” English: A set is a well defined collection of objects.
The elements or members of a set can be anything: numbers, characters, words, names, letters of the alphabet, even other sets, and so on. Sets are usually denoted with capital letters. This is not the exact mathematical definition, but it is good enough for the following.