Overview
Paradoxes that were discovered in mathematics (particularly Russells paradox below) were the primary motivation for the formal development of set theory.
Russells Paradox
Ruseells paradox arises when one asks whether the set that contains all the sets which dont include themselves, acutally contains itself. Formal Definition
{% R = \{x| x\notin x\} %}
Then the paradox arises when asking if {% R \in R %}?