It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same. Therefore, learning about iterated products of double products will help the understanding of the rearrangements of products. In the absence of simple examples, existence theorems lend little confidence to understanding. In this article several inspiring examples are presented to show that infinite products indeed behave very differently from finite products as is the case with infinite sums.