There is another equivalent definition of computable numbers via computable Dedekind cuts. A computable Dedekind cut is a computable function D {\displaystyle D\;} which when provided with a rational number r {\displaystyle r} as input returns D ( r ) = t r u e {\displaystyle D(r)=\mathrm {true} \;} or D ( r ) = f a l s e {\displaystyle D(r)=\mathrm {false} \;} , satisfying the following conditions: