No. Integers are positive and negative whole numbers (…, -2, -1, 0, 1, 2, …). As there are an infinite number of negative integers as they approach negative infinity (the greatest negative integer being -1), there can be no smallest (negative) integer.
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The smallest 5 digit integer is -99999. The largest 5 digit integer is 99999. The sum is therefore 0.
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.
-1: Negative integers become smaller as their absolute value increases. Therefore, the first negative integer is the smallest. This answer assumes that -0 is excluded because 0 is neither positive nor negative.
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