Describing real numbers as a set is useful but it is not very helpful. We need a way to represent that the set of all the real numbers is an ordered set, because if we compare any two numbers, one will always be bigger than the other.
Your class can be made into an ordered set by arranging all the learners alphabetically. This can also be done differently, e.g. by date and time of birth, by shoe size, by weight etc. Number sets are usually only ordered according to their values.
The way we do this is to imagine that each and every real number is a point on a line, called the number line.