Set theory is a branch of mathematics that uses rules to construct sets. In 1901, Bertrand Russell explored the generality and over-permissiveness of the rules in set theory to arrive at a famous contradiction: the well-known Russell's paradox. The echoes of Russell's Paradox resonate beyond mathematics in fields like software systems, where rules are usually used to design such systems. When the rules that we use to build our systems are naive or over-permissive, we open the door for edge cases that may be hard to deal with. After all, to deal with Russell's paradox, mathematicians had to rethink the foundations of set theory and develop more restrictive and rigorous axiomatic systems, like Zermelo-Fraenkel's set theory.
Russell's Paradox Explained
The rule that created all the problems was the following: A set can be made of anything that we can think of. This is formally known as unrestricted composition. To make things easier for Russell in finding an interesting edge case, there was a rule that stated that sets can contain themselves.