# Category:Real Multiplication

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This category contains results about Real Multiplication.

The multiplication operation in the domain of real numbers $\R$ is written $\times$.

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 $x \times y$ is defined as:

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

## Subcategories

This category has the following 7 subcategories, out of 7 total.

### M

### N

## Pages in category "Real Multiplication"

The following 34 pages are in this category, out of 34 total.

### M

- Multiplication by Negative Real Number
- Multiplication by Negative Real Number/Corollary
- Multiplication of Positive Number by Real Number Greater than One
- Multiplication of Real Numbers Distributes over Subtraction
- Multiplication of Real Numbers is Left Distributive over Subtraction
- Multiplication of Real Numbers is Right Distributive over Subtraction

### N

### P

- Pointwise Multiplication on Real-Valued Functions is Associative
- Pointwise Multiplication on Real-Valued Functions is Commutative
- Positive Real Axis forms Subgroup of Complex Numbers under Multiplication
- Positive Real Numbers Closed under Multiplication
- Product of Negative Real Numbers is Positive
- Product of Quotients of Real Numbers
- Product of Real Number with Quotient
- Product of Real Numbers is Positive iff Numbers have Same Sign
- Product of Reciprocals of Real Numbers
- Product of Strictly Positive Real Numbers is Strictly Positive

### R

- Real Multiplication Distributes over Addition
- Real Multiplication Identity is One/Corollary
- Real Multiplication is Associative
- Real Multiplication is Closed
- Real Multiplication is Commutative
- Real Multiplication is Well-Defined
- Real Number Ordering is Compatible with Multiplication
- Real Numbers under Multiplication do not form Group
- Real Numbers under Multiplication form Monoid