## Dedekind’s Theory of Real Numbers

Intro Let $\mathbf{Q}$ be the set of rational numbers. It is well known that $\mathbf{Q}$ is an ordered field and also the set $\mathbf{Q}$ is equipped with a relation called "less than" which is an order relation. Between two rational numbers there exists an infinite number of elements of $\mathbf{Q}$. Thus, the system of rational numbers seems to be dense and so apparently complete. But it is quite easy to show that there exist some numbers (?)…