No. It has a discontinuity at every integer value.
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.
Less than
Neither of the two are one-to-one
yes
Inverse of a function exists only if it is a Bijection. Bijection=Injection(one to one)+surjection (onto) function.
piecewise
it means something great and top fave to grades
The most common example of the Greatest Integer Function is the Post Office. Postage is paid based on weight. For example, from between 1 and 2 ounces, you might pay $1.25 postage. However, when you hit 2 ounces to almost 3 ounces you pay $2.00. This progression is a greatest integer function and is currently used today by the Post Office. You could probably get their rate chart and see.
No, because there is no greatest integer.
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.
There is no greatest integer. Whatever integer you think is greatest, you can always add one (1) to it and get a larger one.