1.2. Relations and Functions
- What is the preimage of R ? What is the preimage of [-1/2, 1/2] ?
The preimage of [-1/2, 1/2] consists of all elements such that f(x) is contained in [-1/2, 1/2]. This set does not contain 1, so the preimage of that set can not contain any irrational number. Hence, the preimage of [-1/2, 1/2] is the set of rational numbers Q.