Set of Numbers

Sets of Numbers

Positive integers
$\mathbb{Z}^{+} = \set{1,2,3,4,...}$
Natural integers
$\mathbb{N} = \set{0,1,2,3,4,...}$
Negative integers
$\mathbb{Z}^{-} = \set{-1,-2,-3,-4,...}$
Integers
$\mathbb{Z} = \mathbb{Z}^{-} \cup \set{0} \cup \mathbb{Z}^{+}$
Rational numbers
$\mathbb{Q} = \set{\frac{p}{q} | q \not = 0 \land p, q \in \mathbb{Z}}$
Irrational numbers
Limits of sequences of rational numbers (which are not rational numbers)
Real numbers
$\mathbb{R} = \mathbb{Q}^{c} \cup \mathbb{Q}$

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

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

\forall y\in\mathbb{R^+} \; \exists k \in \mathbb{Z}^+ \; \text{s.t.} \; \frac{1}{k} \lt y

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September 13, 2026 1 min read

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