# Category:Extended Real Numbers

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This category contains results about **Extended Real Numbers**.

Definitions specific to this category can be found in Definitions/Extended Real Numbers.

The **extended real number line** $\overline \R$ is defined as:

- $\overline \R := \R \cup \set {+\infty, -\infty}$

that is, the set of real numbers together with two auxiliary symbols:

- $+\infty$,
**positive infinity** - $-\infty$,
**negative infinity**

such that:

- $\forall x \in \R: x < +\infty$
- $\forall x \in \R: -\infty < x$

## Subcategories

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

### E

- Extended Real Number Space (2 P)

## Pages in category "Extended Real Numbers"

The following 15 pages are in this category, out of 15 total.

### E

- Extended Real Addition is Associative
- Extended Real Addition is Commutative
- Extended Real Multiplication is Associative
- Extended Real Multiplication is Commutative
- Extended Real Numbers under Multiplication form Commutative Monoid
- Extended Real Numbers under Multiplication form Monoid
- Extended Real Sigma-Algebra Induces Borel Sigma-Algebra on Reals