 Type 1 computability is the naive form of computable analysis in which one restricts the inputs to a machine to be computable numbers instead of arbitrary real numbers.The difference between the two models lies in the fact that a function which is well-behaved over computable numbers (in the sense of being total) is not necessarily well-behaved over arbitrary real numbers.For instance, there are continuous and computable functions over the computable real numbers which are total, but which map some closed intervals to unbounded open intervals.