Modulo Operation/Examples/1.1 mod 1

Theorem

 * $1 \cdotp 1 \bmod 1 = 0 \cdotp 1$

where $\bmod$ denotes the modulo operation.

Proof
By definition of modulo $1$:
 * $x \bmod 1 = x - \left \lfloor {x}\right \rfloor$

Thus: