Sawtooth and replicative functions

Here’s something I ran across in Volume 2 of Donald Knuth’s The Art of Computer Programming. Knuth defines the sawtooth function by ((x)) = x – (⌊x⌋ + ⌈x⌉)/2. Here’s a plot. This is an interesting way to write the sawtooth function, one that could make it easier to prove things about, such as the […] The post Sawtooth and replicative functions first appeared on John D. Cook....

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