No. Never.
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No, the sum of two negative integers is not a positive integer. For example, if you add -5 and -6 together the sum would be -11.
sum of positive integers will be a positive integer
The statement is: "Their sum is always an integer." Whether the sum is negative or positive depends on the two original integers.
Yes, the sum of two negative integers is always negative.
The sum of a negative integer and a positive integer is zero only when the two integers have the same absolute value. For example, if you have -3 (negative integer) and +3 (positive integer), their sum is zero. However, in general, this situation occurs infrequently since it requires specific values. Most of the time, the sum will be a negative integer if the absolute value of the negative integer is greater than that of the positive integer, and a positive integer if the opposite is true.