Chapter 5.2, Problem 7MC

The Swiss mathematician Leonhard Euler (1707-1783) argued that $(-1)(-1)=1$ as follows: “the result must be either $-1$ or $1$. If it is $-1$, then $(-1)(-1)=-1$. Because $-1=\left(-1\right)1$, we have $(-1)(-1)=(-1)1$. Now dividing both sides of the last equation by $-1$, we get $-1=1$, which of course cannot be true. Hence $(-1)(-1)$ must be equal to $1$.”

a. What is your reaction to this argument? Is it logical? Why or why not?

b. Can Euler’s approach be used to justify other properties of the integers? Explain.