No, it is not possible to write a pair of integers whose sum is not an integer.
The fundamental property of integers guarantees that when you add any two integers together, the result will always be another integer. This is a core concept in mathematics.
Why the Sum of Two Integers is Always an Integer
Integers are whole numbers (not fractions or decimals) and can be positive, negative, or zero. Adding two whole numbers will always result in another whole number.
- Example 1: 5 + 3 = 8 (Both 5 and 3 are integers, and their sum, 8, is also an integer).
- Example 2: -2 + 7 = 5 (Both -2 and 7 are integers, and their sum, 5, is also an integer).
- Example 3: -4 + -6 = -10 (Both -4 and -6 are integers, and their sum, -10, is also an integer).
Understanding the Reference
The reference states that the given statement is false. This directly supports the answer that you cannot write a pair of integers whose sum is not an integer. The act of summing integers is closed under the operation of addition; it always produces another integer.
Conclusion
The statement "Can we write a pair of integers whose sum is not an integer?" is definitively false. The sum of any two integers will invariably result in an integer.
