The integers less than or equal to 2 are: {2, 1, 0, -1, -2, -3, ...}
10, 8, 6, 4, 2, 0 and all the negative even integers.
Seven of them.
All integer less than or equal to 3 would actually be infinite. It would start at 3 and would keep decreasing in value. 3, 2, 1, 0, -1, -2, and so on forever.
3, 2, 1
6
That happens when only one of the two integers is negative.
10, 8, 6, 4, 2, 0 and all the negative even integers.
Seven of them.
The integers that are greater than -2 but less than 5 are: -1, 0, 1, 2, 3, 4
The odd integers less than 5 are 1 and 3. Therefore, there are 2 odd integers that meet this criterion.
17
All integer less than or equal to 3 would actually be infinite. It would start at 3 and would keep decreasing in value. 3, 2, 1, 0, -1, -2, and so on forever.
1 and 2
There are no negative integers greater than 2. Negative integers are less than zero, while the integer 2 is positive. Therefore, the set of negative integers consists of numbers like -1, -2, -3, and so on, which do not exceed 2.
-2 is less than 2
A counterexample to the statement "the difference of two integers is less than either integer" can be demonstrated with the integers 5 and 3. The difference is (5 - 3 = 2). Here, 2 is not less than either integer, as it is less than 5 but greater than 3. Thus, this example shows that the difference can be less than one integer but not the other.
3, 2, 1