Bases Unboxed: The Basis Representation Theorem and the Uniqueness of Numbers

In this episode, we explore why every positive integer has a unique representation in any base b — from decimal to binary to hexadecimal. We build intuition with lego-like imagery, sketch the idea behind a concise induction-style proof of uniqueness, and connect the concept to computing and to alternative number systems like prime or Fibonacci bases. A practical and theoretical tour of a foundational theorem that underpins how we understand and manipulate numbers.

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