Modulo Operation/Examples/0.11 mod -0.1

Theorem

 * $0 \cdotp 11 \bmod -0 \cdotp 1 = -0 \cdotp 09$

where $\bmod$ denotes the modulo operation.

Proof
By definition of modulo operation:
 * $x \bmod y := x - y \left \lfloor {\dfrac x y}\right \rfloor$

for $y \ne 0$.

We have:

and so:
 * $\left\lfloor{\dfrac {0 \cdotp 11} {-0 \cdotp 1} }\right\rfloor = -2$

Thus: