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.
No. It has a discontinuity at every integer value.
Neither of the two are one-to-one
The absolute value of an integer is the integer with no sign. The absolute value of +3 and -3 is 3.
Inverse of a function exists only if it is a Bijection. Bijection=Injection(one to one)+surjection (onto) function.
No, because there is no greatest integer.
There is no greatest integer. Whatever integer you think is greatest, you can always add one (1) to it and get a larger one.
The smallest positive integer is 1. 1 is the multiplicative identity; ie anything times 1 is itself. The greatest negative integer is the most positive negative integer which is -1. Therefore the product of the greatest negative integer and the smallest positive integer is the greatest negative integer which is -1.