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[] denotes the greatest integer less than or equal to.
Ex: [2.45] = 2, [-2.1] = -3, [1.75] = 1, [0.32] = 0, etc.
Now, [x] - [-x] = x - (-x - 1)
= x + x + 1
= 2x + 1
= 2[x] + 1