Goodstein's theorem is a result in mathematical logic and number theory that deals with a particular sequence of natural numbers known as Goodstein sequences. The theorem states that every Goodstein sequence eventually terminates at 0, despite the fact that the terms of the sequence can grow extremely large before reaching 0. To understand Goodstein's theorem, we first need to define how a Goodstein sequence is constructed: 1. **Starting Point**: Begin with a natural number \( n \).
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