Thus, e.g., if a0, a1, a2, a3, … is an infinite sequence of real numbers, then the infinite product  is defined, and equal to  if and only if that limit exists.
In other words, for example, if we have an infinite series of real numbers a0, a1, a2, a3, …, then the infinite product is established, and it equals  if and only if the aforementioned limit exists.