Set of Numbers

Sets of numbers

• Positive integers: .
• Natural integers: .
• Negative integers: .
• Integers: .
• Rational numbers: .
• Irrational numbers: limits of sequences of rational numbers (which are not rational numbers)
• Real numbers: .

Complex numbers are taught in a separate set of lectures, and not included under real analysis lectures.

Axiomatic definiton of real numbers

Set of real numbers is a set satisfying all these axioms:

• Field axioms
• Order axioms
• Completeness axiom

Archimedean property