Amos Fourteen

Amos 14

The girl reads by streetlight though the open curtain so as not to disturb her younger sister sleeping. She reads about transcendental functions, the inverse functions of calculus. The girl has just turned fourteen, yet she follows the text easily: Let A be an open interval and let f : A → R be injective and continuous. Then f−1 is continuous on f(A).” The assignment calls for a proof. On her notebook she writes in pencil: “Proof. Since A is an open interval and f is injective and continuous it follows that f has no local maxima or minima. Therefore, f is either strictly increasing or strictly decreasing.” Or perhaps both, she wonders. No, that cannot be right. She has no friend she might ask, no one in her family who might know. She sleeps and dreams of the continuous stripes on a small zebra, the open and infinite space of reversibility. 

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