Here is the definition of the fixed point. Again you see it is very easy to define a fixed point implicitly. Look at the stream of seasons. Here, what are seasons? Season is not just the list of spring, summer, autumn and winter, but it is the process, the never-ending process of having new seasons, and this is captured by a recursive definition. Here is the stream of all natural numbers. And look at this, the natural number is bigger than n is a stream whose first element is n and whose second element is the set of natural numbers bigger than n plus 1.