In set theory there are two wings of study, the axiomatic and the naive theory. The axiomatic wing relies on an informal understanding of sets as collections of objects. The naïve approach, well developed at the end of the 19th century, treats sets as demonstrable forms with propositions, lemmas, theorems and corollaries. Set theory is very important in mathematics, especially for modern theory such as: numbers relations functions Specification axiom Axioms are fundamental to mathematics. However, when we assume that any operations on sets can lead to paradoxes such as Russell’s paradox. Axiomatic theory was fundamental in determining which operations are allowed for sets.