Idempotency of Transfinite Cardinal Numbers

Key Points

• The aim is to provide a clear proof of the idempotency of transfinite cardinal numbers using Zorn's lemma suitable for undergraduates.
• Utilized Zorn's lemma as a key tool in the proof process.
• Presented the proof in an accessible manner for undergraduate students.
• Focused on illustrating the relationships between addition and multiplication of transfinite cardinals.
• Demonstrated that α + α = α for transfinite cardinal α.
• Proved that αα = α also holds true for transfinite cardinal α.
• Established a clear understanding of idempotency in the context of transfinite cardinals.