But in 1972, Bill Gosper solved the problem of general arithmetic on continued fractions
Suppose x is a continued fraction, possibly infinite
Think of it as an object (in the sense of "object-oriented programming")
There is a method we can use to ask it for its next term
When we do this, it will also modify its internal state
Next time we ask for the next term, we get the next next term
Terms might be stored internally, or might be computed only on demand
If we only need a certain amount of precision, we can stop reading after a while
The work to calculate the remaining terms will not be done until we need it