Chapter 1.3, Problem 58HP

To determine

Whether 1 can be considered as additive identity or not, explain with an example.

Answer to Problem 58HP

No, 1 cannot be as additive identity as $4+1\ne 4$ .

Explanation of Solution

The additive identity property states that the addition of any real number with zero will give the same number itself, that is, $0+a=a+0$ will give the same number $a$ .

Consider a number $a$ as $4$ .

Use the additive identity to add 4 and 1 as follows:

  $\begin{array}{r}4+1\stackrel{?}{=}4\\ 5\ne 4\end{array}$

Thus, 1 cannot be as additive identity as $4+1\ne 4$ .