chapter 2Facts about Functions

Leibniz himself attributed all of his mathematical discoveries to improvements in notation.

— Gottfried Wilhelm von Leibniz (1646–1716)

From The Nature of Mathematics by Philip E. B. Jourdain

Leibniz introduced the word “function” to mathematics around 1692. Functions can often make life simpler. This chapter will start with the basic notions and notations for functions, focusing on mathematical functions that are especially important in computer science: floor, ceiling, gcd, mod, and log. We’ll cover the technique of composition for constructing new functions from simpler ones. Three important properties of functions—injective, surjective, and bijective—and how these properties apply to the pigeonhole principle, ...

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