# Number Sets

# Natural Numbers

Natural numbers are a set, which is creating by starting at 0 and each new element is created by adding one to the previous one.

N=def{0,1,2,3,4,5,… }\mathbb{N} \stackrel{def}{=} \{0, 1, 2, 3, 4, 5, \dots\}

# Whole Numbers

Whole numbers are naturals numbers with their additive inverses.

Z=def{…,−3,−2,−1,0,1,2,3,… }\mathbb{Z} \stackrel{def}{=} \{\dots, -3, -2, -1, 0, 1, 2, 3, \dots\}

# Rational Numbers

Rational numbers are numbers which can be expressed as a fraction of two whole numbers.

Q=def{pq  ∣  p,q∈Z}\mathbb{Q} \stackrel{def}{=} \{\frac{p}{q} \,\,|\,\, p, q \in \mathbb{Z}\}