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\begin{document}
	\chapter{Axioms}
	\begin{enumerate}
		\item $\mathbb{C} \supset \Re$ \\ The set of complex numbrs are a proper superset of all real numbers.
		\item $\forall s \in \mathbb{C} ( s = a + ib \wedge i = \sqrt{-1} \wedge a \in \Re \wedge b \in \Re)$ \\ It is true that for all numbers s in the set $\mathbb{C}$ that $ i = \sqrt{-1}$ and that a is a real number and that b is a real number.
		\item $\forall s \in \mathbb{C}$ (Re(s) = a $\wedge$ Im(s) = b) \\ The function Re applied to any complex number s will return the real part a, and the function Im will return the imaginary part b.
		\item $ ib \in s \perp a \in s $ \\ All values bi exists in a dimension perpendicular to $\Re$. All values in $\mathbb{C}$ exists in a plane, where one axis is the real coordinate and the imaginary component of s is regarded as ocupying another coordinate axis in a cartesian coordinate system.
		\item $\exists s \in \mathbb{C} (s = 0 \wedge s = 0 + 0i) $ \\ There exists an elemment s in $\mathbb{C}$ such that s is null and the meaning of this is that a = 0 and b = 0. This is called the null element.
		\item $\exists s \in \mathbb{C} (s = 1 \wedge s = 1+0i) $ \\ There exists an element s in $\mathbb{C}$ such that s is 1 and the meaning of this is that a = 1 and b = 0. This is 
	\end{enumerate}
\end{document}