Neither of the two are one-to-one
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Both the Greatest Integer Function and the Absolute Value Function are considered Piece-Wise Defined Functions. This implies that the function was put together using parts from other functions.
piecewise
The absolute value of an integer is the integer with no sign. The absolute value of +3 and -3 is 3.
Subtracting a negative integer is the same as adding its absolute value.
No - the absolute value of any integer is either the integer itself or its positive equivalent, if negative.