Interactive Real Analysis1.1. 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}
E,
O 
I,
comp(I).
back- 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).