Final answer:
Jesus did not preach throughout Rome and Greece; this task was primarily carried out by his follower Paul. Paul's mission significantly altered Roman society by introducing a religion based on the worship of a single God that contradicted the prevailing polytheistic norms.
Step-by-step explanation:
The belief that Jesus preached throughout Rome and Greece is False. Jesus of Nazareth preached primarily in the region of Israel. However, after his death, his followers, especially Paul (who is known for his conversion on the road to Damascus and never met Jesus), became instrumental in spreading Christianity throughout the Greek and Roman cities of the Mediterranean, including Ephesus, Corinth, Thessalonica, and Rome itself.
This expansion of Christianity was significant in the transformation of the social and religious fabric of the Roman Empire, allowing it to reach a broad audience and increasingly gain acceptance within Roman society. Christianity's spread during the Roman Empire signified a shift from polytheistic practices to the worship of a single God, offering a sense of inclusivity and hope to groups such as slaves.
This was in stark contrast to the traditional Roman religious authority, which eventually led to persecution of Christians. Nonetheless, the acceptance of Christianity by Roman emperors, most notably Constantine, paved the way for the religion's legitimization and integration into Roman culture, significantly altering the society from its earlier state.