Borel sets of the Real Line

The Borel Sets of the real line can be generated in a number of ways.

1. The open intervals
2. The closed intervals
3. The half-open intervals
4. The half-open intervals
5. The open rays
6. The open rays
7. The closed rays
8. The closed rays

Proof

It is clear that for . It is enough to show that , which will show that , completing our proof.