Happiness Is Integral But Not Rational
Math Horizons, Sep 1, 2017
That is, every natural number has a path that reaches one of the components in figure 1. See Ross... more That is, every natural number has a path that reaches one of the components in figure 1. See Ross Honsberger’s Ingenuity in Mathematics (Random House, 1970, pages 83–84) for a proof of this fact. A number is called happy if it eventually reaches 1 and unhappy otherwise. In this article we explore happiness in several different numeral systems. We include exercises along the way that we hope will enhance your experience. The proofs-based exercises are meant to extend the ideas we present and are completely optional. We also include a few example-driven exercises that we strongly encourage you to complete, as they will be important later in the article.
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