## 1.1. Notation and Set Theory

### Examples 1.1.2(c):

- E = { x: x = 2n for n N }
- O = {x : x = 2n - 1 for n N }
- I = {x R: x * x = -2}

**O****E**is the set of all natural numbers that are even or odd. Hence**O****E**=**N**.**O****E**is the set of all natural numbers that are both even and odd. Hence**O****E**=**0**(empty set)- comp(
**I**) is the set of all numbers that are not in**I**. Since**I**is empty, it is the set of numbers that are not in the empty set. Hence: comp(**I**) =**R**(here again the universe is understood to be all real numbers).