What is happening here? Why is the first calculation returning an integer, but not the second calculation? What are the rules for computing mod for floats and negative numbers?
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Have you tried reading the Wikipedia article on modulo? – john_leo Oct 21 '14 at 08:53
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I just think it extended classic rules. $$2\times\frac{21}{2} - 16 = 5$$ So $-16 = 5 \mod \frac{21}{2}$
A. Breust
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Mathematically $x\bmod y$ means $x-ky$ with $k\in\Bbb Z$ such that $ky$ is the largest integer multiple of $y$ for which $ky\leq x$ (at least this is the definition when $y>0$; when $y<0$ conventions vary). In your example $k=-2$ both times, so $ky=-21$ respectively $ky\approx-21.069$.
By the way, most computer hardware designers either didn't understand the mathematical meaning of $\bmod$ our found it too hard to implement, so that most computer hardware implements a different remainder operation (at least when $x,y$ are integers). See here. But the calculator software does seem to get it right here.
Marc van Leeuwen
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