Explore relationships

Transitive class

In set theory, a branch of mathematics, a setA{\displaystyle A} is called transitive if either of the following equivalent conditions holds: whenever x∈A{\displaystyle x\in A}, and y∈x{\displaystyle y\in x}, then y∈A{\displaystyle y\in A}.whenever x∈A{\displaystyle x\in A}, and x{\displaystyle x} is not an urelement, then x{\displaystyle x} is a subset of A{\displaystyle A}.Similarly, a classM{\displaystyle M} is transitive if every element of M{\displaystyle M} is a subset of M{\displaystyle M}.

Use + to expand a branch. Click a topic name to open its summary.