Standard Number System

There are some standard number systems we gotta keep in mind. They are sets of numbers where

{1,2,3,...}⊆N{...,−3,−2,−1,0,1,2,3,...}⊆Z{pq∀p∈Z,q≠0}⊆Q{2,π,...}∈R{3+1i,5+5i,2+0i}∈C=F\begin{gather*} \{1,2,3,...\}\subseteq\mathbb{N}\\ \{...,-3,-2,-1,0,1,2,3,...\}\subseteq\mathbb{Z}\\ \{\frac{p}{q}\quad\forall p\in \mathbb{Z},q\neq 0 \}\subseteq\mathbb{Q}\\ \{\sqrt{2},\pi,...\}\in \mathbb{R}\\ \{3+1i, 5+5i, 2+0i\}\in\mathbb{C}=\mathbb{F} \end{gather*}

Where

  • N\mathbb{N} are natural numbers

  • Z\mathbb{Z} are integers

  • R\mathbb{R} are real numbers

  • C\mathbb{C} are Complex Number, F\mathbb{F} are fields

where ∀p∈Z,q≠0\forall p\in \mathbb{Z},q\neq 0 means for all integers pp AND q≠0q\neq 0