The urgency of defining heresy

Christianity and Judaism eventually split in a fundamental way. To help us explore that rift, we'll focus on the following questions:

1. If the early Christians were Jewish and early Christianity was similar to Judaism, when and why did Christians develop such animosity towards Jews?
2. How did the Romans relate to the Christians?
3. Why was it so important for the Council of Nicaea to define Christianity and its heresies?