Characteristic¶
The characteristic of a finite field \(F\) is the smallest positive number \(n\) such that the sum of the multiplicative identity \(1\) repeated \(n\) times result in the additive identity \(0\). This is expressed as:
\[
\begin{aligned}
1 + 1 + ... + 1 = 1 \cdot n = 0
\end{aligned}
\]
For example, if the field has characteristic \(2\), it means that:
\[
\begin{aligned}
1 + 1 = 0
\end{aligned}
\]