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20 December 2024
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Replaced content with "File:Collatz formal.pdf"
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Replaced content with "== Proof of Predictability == To prove the **predictability** of the Collatz conjecture, we demonstrate that for any starting number \( n \), we can predict when the sequence will produce a number smaller than \( n \). This involves analyzing the transformations \( n \to \frac{n}{2} \) (for even numbers) and \( n \to \frac{3n + 1}{2} \) (for odd numbers). === Step 1: Transformation Behavior === ==== Case 1: \( n \) is even ==== When \( n \) is even: \[ n \to \frac..."
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