The integer greater than -3 and less than 2 is -2. This is because it is the largest integer that is greater than -3 but still less than 2. In the number line, -2 falls between -3 and 2.
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0 1 2 3 4
5 > (greater than) 2 2 < (less than) 5
-2 is less than 2 -2 < 2
The solution is that a is any number: integer, rational or irrational, that is greater than 2. There is no other way of putting it.
Positive integers are the counting numbers (1, 2, 3, 4, 5 and so on) greater than zero. Negative integers are their counterparts (-1, -2, -3, -4, -5 and so on) less than zero.