[[Dedekind-MacNeille completion]]
# Extended real line

The **extended real line** $[-\infty,\infty]$ consists of the [[real numbers]] with additional elements $\{ -\infty,\infty \}$ such that $-\infty \leq x \leq \infty$ for all $x \in \mathbb{R}$ $\infty \geq x$. #m/def/anal 
Thus it is the [[Dedekind-MacNeille completion]] of the reals and the rationals.


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