# Category:Real Number Line with Euclidean Metric

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This category contains results about **Real Number Line with Euclidean Metric**.

Definitions specific to this category can be found in Definitions/Real Number Line with Euclidean Metric.

On the real number line, the Euclidean metric can be seen to degenerate to:

- $\map d {x, y} := \sqrt {\paren {x - y}^2} = \size {x - y}$

where $\size {x - y}$ denotes the absolute value of $x - y$.

## Subcategories

This category has the following 2 subcategories, out of 2 total.

## Pages in category "Real Number Line with Euclidean Metric"

The following 18 pages are in this category, out of 18 total.

### O

- Open Ball in Real Number Line is Open Interval
- Open Rational-Number Balls form Neighborhood Basis in Real Number Line
- Open Real Interval is not Closed Set
- Open Real Interval is not Closed Set/Corollary
- Open Real Interval is Open Ball
- Open Reciprocal-N Balls form Neighborhood Basis in Real Number Line
- Open Sets in Real Number Line