Collatz Inequality and Singleton Expansion

I've blogged about this gem from Lothar Collatz (1910-1990) before, but it deserves to be repeated. Especially since it now provides an elegant example of singleton expansion.

For $|x|,|y| \le 4$

$$ ||||x| - 1| - 1| - |||y| - 1| - 1|| < \frac{1}{3} $$

Compare today's code code with this.

    x = -4:1/64:4;
    v = abs(abs(abs(x)-1)-1);
    z = abs(v - v') < 1/3;
    spy(z)
    noticks




Published with MATLAB® R2020a

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