Given x is a real number and c is a natural number. Prove that:
floor( floor(x) / c ) = floor( x / c )
When x > 0, I can prove it by let x = n + z where 0 < z < 1.
Then rhs = floor( n/c + z/c ) which equals to floor( floor(x) ) since z/c -> 0.
However, when x < 0, it's wrong when letting x = -( n + z ). Because it always give me a smaller negative number. Is my logic wrong here? Any hint?
Thanks,
Chan