The Burali-Forti Paradox is a paradox in set theory related to the concept of ordinals. It arises when considering the set of all ordinals. Ordinals are a type of mathematical object that generalize the concept of counting numbers and are used to describe the order type of well-ordered sets.
The paradox can be summarized as follows:
1. **Assumption of a Set of All Ordinals**: Suppose there exists a set \( O \) that contains all ordinals. This


