On an orbital research station, Emek and Tara discovered that the navigation computer had scrambled its number system map. Five values were waiting to be classified: 14, -7, 3.25, 5/8, and sqrt(11). Emek placed 14 with the natural numbers and noted that it was also an integer and a rational number. Tara classified -7 as an integer and therefore also rational. They recognized that 3.25 and 5/8 were rational because each could be written as a fraction of integers. The final value, sqrt(11), could not be written as such a fraction, so they placed it with the irrational numbers. Tara checked the map's structure: natural numbers belonged inside the integers, and integers belonged inside the rational numbers, while rational and irrational numbers were separate parts of the real numbers. With every value correctly placed, the computer accepted the repaired map and restored the station's navigation calculations.




