Question

Find a pair of integers whose difference is \[2\]?

Answer 1

Hint: We know that there are infinite numbers in the number system and hence we can find an infinite number of pairs of integers whose difference would be \[2\]. We can also find it randomly or else using the linear equations in a single variable.

Complete step-by-step solution:
Now let us learn the properties of integers. Integers are nothing but the number system that includes zero, negative numbers as well as the positive numbers. Zero is considered to be neither a positive nor negative number. Integers follow the commutative property, associative property, identity property and also the closure property.
Now let us find the pair of integers whose difference is \[2\].
Let us consider \[x\] as the largest integer and \[x-2\] would be the smallest integer from the two random integers considered.
We can find the pair of integers by adding these two integers or else by subtracting the integers considered.
Firstly let us add the integers considered. We get,
\[\begin{align}
  & x+\left( x-2 \right)=0 \\
 &\Rightarrow 2x=2 \\
 &\Rightarrow x=1 \\
\end{align}\]
Now upon substituting the value of \[x\] in the equation considered, we get a pair of integers whose difference is \[2\].
Upon substituting, we get
\[\begin{align}
  & x=1 \\
 &\Rightarrow x-2=1-2 \\
 & \Rightarrow -1 \\
\end{align}\]
The first pair we obtain would be \[\left( -1,1 \right)\].
We can consider some of the integers whose difference would be \[2\]. They are:
\[\left( -5,-3 \right),\left( 7,9 \right),\left( -2,0 \right),\left( 0,2 \right)\] etc.

Note: We must note that as the value of the negative numbers increases, it means that the numbers are actually getting smaller. The negative integer that is nearer to zero is greater than the integer that is away from zero. Zero always retains its properties in whichever the number system it is being included.