No. Just like positive integers, negative integers stretch out to infinity. There will never be a least negative integer.
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a negative integer
The negative three-digit number with the least value is -999.
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.
A negative number can be an integer. An integer is any positive or negative whole number including zero.
Subtracting a negative is like adding a positive.