# Category:Real Addition

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This category contains results about **Real Addition**.

The addition operation in the domain of real numbers $\R$ is written $+$.

From the definition, the real numbers are the set of all equivalence classes $\eqclass {\sequence {x_n} } {}$ of Cauchy sequences of rational numbers.

Let $x = \eqclass {\sequence {x_n} } {}, y = \eqclass {\sequence {y_n} } {}$, where $\eqclass {\sequence {x_n} } {}$ and $\eqclass {\sequence {y_n} } {}$ are such equivalence classes.

Then $x + y$ is defined as:

- $\eqclass {\sequence {x_n} } {} + \eqclass {\sequence {y_n} } {} = \eqclass {\sequence {x_n + y_n} } {}$

## Subcategories

This category has the following 3 subcategories, out of 3 total.

### A

### R

## Pages in category "Real Addition"

The following 16 pages are in this category, out of 16 total.

### P

### R

- Real Addition Identity is Zero
- Real Addition Identity is Zero/Corollary
- Real Addition is Associative
- Real Addition is Closed
- Real Addition is Commutative
- Real Addition is Well-Defined
- Real Multiplication Distributes over Addition
- Real Number Ordering is Compatible with Addition
- Real Numbers under Addition form Monoid