A Proof of the 3x-1 Conjecture

Key Points

• The aim is to establish the validity of the 3x-1 conjecture.
• Utilized the same methodology as the Collatz conjecture proof.
• Analyzed the complete odd-to-odd map for large odd integers.
• Showed that trajectories eventually enter one of three known cycles.
• Confirmed that the odd-to-odd map strictly decreases for all sufficiently large odd integers.
• Established the inevitability of trajectories converging to known cycles.