I am not at all sure that there are any rules that apply to integers in isolation. Any rules that exist are in the context of binary operations like addition or multiplication of integers.
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No. An integer is a WHOLE number. A number with a decimal place or a fraction is not an integer :)
Any integer can be divided by any non-zero integer, and the result is a rational number.
Well, the square root of 25 is five, and 5 is an integer, yes.
A positive integer divided by a positive integer always results in a positive quotient. It is not possible to divide by zero.
The value of the greatest integer is 76. This occurs when the set of five consecutive integers is all even numbers.