If a finite model satisfies all the same equational laws as the integers, then no individual equational law distinguishes the integers as infinite.

(i) It could tell us to what extent the equational laws holding of the integers characterize the integers. Since the set \(\{0, 1\}\) of integers mod 2 under addition and negation satisfies all the laws that the integers do, we immediately see that no single equational property of the integers tells us that there are infinitely many integers. On the other hand any finite model of the equational theory of the integers necessarily satisfies some law that the integers don’t satisfy, in particular t