Question

Write down a pair of integers whose sum is 0.

Answer 1

Hint: In the given question, we have been asked to write two integers whose sum is zero. Now, consider there is a number. Then, we have another number which when added to the first number gives a zero. This second number is called the additive inverse of the first number and vice-versa. So basically, we have to find two numbers which are additive inverses of each other.

Complete step-by-step answer:
In the given question, we have been asked to write two integers whose sum is zero. We know that such numbers are called additive inverses of each other.
Now, consider there is a number \[n\]. Then, the additive inverse of \[n\] is given by,
\[additive{\rm{ \,inverse}} = - \left( n \right) = - n\]
Hence, we just need to write any integer and the other number in the pair can be written by simply inverting the sign of the first integer – negative to positive or if it’s positive, then to negative.
Let the first number of the pair be \[1\], then the second number of the pair is going to be \[ - 1\].
Hence, the two numbers are \[1\] and \[ - 1\].

Note: Now, for finding a pair of integers (or the sets upper than that – rational numbers, irrational numbers or real numbers) having this property, it is possible to find such numbers because they contain negative numbers too. But, if we had to find whole numbers or natural numbers with such property, we wouldn’t have been able to do that because they cannot contain negative numbers in their range, and there needs to be one negative number for such configuration.