\begin{definition}[Definition:Real Number/Real Number Line]
From the Cantor-Dedekind Hypothesis, the set of real numbers is isomorphic to any infinite straight line.
The '''real number line''' is an arbitrary infinite straight line each of whose points is identified with a real number such that the distance between any two real numbers is consistent with the length of the line between those two points.
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Thus we can identify any (either physically drawn or imagined) line with the set of real numbers and thereby illustrate truths about the real numbers by means of diagrams.
\end{definition}