The additive identity of an integer is the number which, when added to any integer, yields the integer itself. Consider any integer [tex]\( n \)[/tex]. The number we are looking for is [tex]\( x \)[/tex] such that:
[tex]\[ n + x = n \][/tex]
The only number [tex]\( x \)[/tex] that satisfies this equation for all integers [tex]\( n \)[/tex] is 0. This is because adding 0 to any number does not change the value of that number. Therefore, 0 is the additive identity of an integer.
To summarize, the additive identity of an integer is 0.
