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Properties of smallest integer function property `(i)[-n]=-[n]where n epsilon N (ii) [-x]=-[x]+1; where xepsilon R-Z (iii) [x+n]=[x]+n where x epsilon R-Z and n epsilon Z (iv) [x]+[-x]={1; x notinZ ; 0 ; xinZ} (v) [x]-[-x]={2[x]-1; xnotinZ ; 2[x] ; if xinZ`

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Properties of Greatest Integer Function (i)[-n]=-[n] (ii)[x+k]=[x]+k (iii) [-x]=-[x]-1 (iv) [x]+[-x]={-1 ; xnotinZ ; 0 ; xepsilonZ} (iv) [x]-[-x]={2[x]+1 ; if xnotinZ ; 2[x] ; if xepsilonZ

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