Download Some Set Theory 1. The set of all natural numbers is the set of all

Some Set Theory
1. The set of all natural numbers is the set of all numbers that you
can count starting from 1. It is denoted by N
N = {1, 2, 3, 4, · · · }
2. The set of all whole numbers is the set of all natural numbers
including 0. It is denoted W
W = {0, 1, 2, 3, 4, · · · }
3. The set of all integers it the following set
Z = {· · · , −2, −1, 0, 1, 2, 3, 4, · · · }
4. The set of all rational numbers is the following set
p
Q = x : x = , and p, q ∈ Z, q 6= 0
q
5. The set of all irrational numbers is the the set of all numbers
that are not rational. It is denoted by I
I = {x : x is not rational}
For example π ∈ I but 2 ∈
/I
6. The set of all real numbers is the set of numbers that are either
rational or irrational. It is denoted by R
R = {x : x is rational or x is irrational}
7. The set of all complex numbers is
C = {x : x = a + ib, where a, b are real number}
Recall that i is the imaginary unit and i2 = −1. Notice that every
real number is a complex number.
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