Field

Define

… as the set

\[\begin{equation*}
  F \supseteq \{0, 1\},
\end{equation*}
\]

in conjunction with the addition operation

\[\begin{gather*}
  \forall a, b \in F, \\[1ex]
  a + b \in F
\end{gather*}
\]

that satisfies all properties listed here

and the multiplication operation

\[\begin{gather*}
  \forall a, b \in F, \\[1ex]
  ab \in F
\end{gather*}
\]

that satisfies all properties listed here.