Counting sort initialization of the output array, each take time. Therefore, the time for the whole algorithm is the sum of the times for these steps, . Because it uses arrays of length and , the total space usage of the algorithm is also . For problem instances in which the maximum key value is significantly smaller than the number of items, counting sort can be highly space-efficient, as the only storage it uses other than its input and output arrays is the Count array which uses space . If each item to be sorted is itself an integer, and used as
Computable number the machine's table – is being used to define what is a potentially-"infinite" string of decimal digits. This is however not the modern definition which only requires the result be accurate to within any given accuracy. The informal definition above is subject to a rounding problem called the table-maker's dilemma whereas the modern definition is not. A real number "a" is computable if it can be approximated by some computable function formula_1 in the following manner: given any positive integer "n", the function produces an integer "f"("n") such that: There are two similar definitions that are equivalent: There is another