Short Answer: Yes.
Integers include the set of counting numbers (1, 2, 3, etc.), their respective negatives (-1, -2, -3, etc.), and 0.
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When you add two negative integers, the answer is still negative.
There are no negative integers greater than five.
One or three.
The set of integers includes negative integers as well as positive integers. It also includes the number zero which is neither negative nor positive.
No. Just like positive integers, negative integers stretch out to infinity. There will never be a least negative integer.