Hi Adam,
Welcome to JavaRanch!
The IEEE floating-point standard, which
Java follows, allows for a couple of special values: NaN (Not A Number), +Inf and -Inf. They're not strings -- they're just specific bit-patterns within the double and float types. There's no way to represent them as a series of digits, because they're not valid numbers, either. The String representation (NaN or Inf or whatever) is created by whatever method does the printing -- i.e., the println() method calls String.valueOf(double) to produce something that it can render to the screen, and it's this method's job to decide how to render the value; it comes up with the strings "NaN" and "+Inf", etc. If you were to write your own method to format doubles, it could do something else for NaN, whatever you wanted it to do.