# What are the six properties of real numbers?

## What are the six properties of real numbers?

Did you know there were so many kinds of properties for real numbers? You should now be familiar with closure, commutative, associative, distributive, identity, and inverse properties.

**What property of real numbers does each statement demonstrate a − a 0?**

inverse property

The inverse property of addition states that, for every real number a, there is a unique number, called the additive inverse (or opposite), denoted−a, that, when added to the original number, results in the additive identity, 0.

### Why is it important that the real numbers have the property of being complete?

Completeness is the key property of the real numbers that the rational numbers lack. Before examining this property we explore the rational and irrational numbers, discovering that both sets populate the real line more densely than you might imagine, and that they are inextricably entwined.

**What is an example of a number property?**

Example: Multiplying by zero When we multiply a real number by zero we get zero: 5 × 0 = 0. −7 × 0 = 0.

## What are sets of real numbers?

Common Sets The set of real numbers includes every number, negative and decimal included, that exists on the number line. The set of real numbers is represented by the symbol R . The set of integers includes all whole numbers (positive and negative), including 0 . The set of integers is represented by the symbol Z .

**What property of real numbers does each statement demonstrate?**

Property (a, b and c are real numbers, variables or algebraic expressions) | |
---|---|

1. | Distributive Property a • (b + c) = a • b + a • c |

2. | Commutative Property of Addition a + b = b + a |

3. | Commutative Property of Multiplication a • b = b • a |

4. | Associative Property of Addition a + (b + c) = (a + b) + c |

### Is the set of real numbers complete?

Axiom of Completeness: The real number are complete. Theorem 1-14: If the least upper bound and greatest lower bound of a set of real numbers exist, they are unique.

**What is completeness property of real numbers?**

Intuitively, completeness implies that there are not any “gaps” (in Dedekind’s terminology) or “missing points” in the real number line. This contrasts with the rational numbers, whose corresponding number line has a “gap” at each irrational value.