No. The positive integers are {1, 2, 3, 4, 5, ...}. They start at 1 (which is the least positive integer) and progress forever (to infinity). There is no end to the positive integers, so there is no greatest positive integer. Another way to look at it might be to think of any really large integer (a "counting" or "whole" number) and add one. That will create a "next bigger" large number. You can continue to do this infinitely many times.
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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 none, because there is always a greater integer.
If the integer subtracted is smaller than or equal to the first integer, then the answer is positive. Otherwise, if the integer subtracted is larger, then the answer is negative.
positive
the positive integer