### All Introduction to Analysis Resources

## Example Questions

### Example Question #1 : Ordered Field And Completeness Axioms

Identify the following property.

On the space where , only one of the following statements holds true , , or .

**Possible Answers:**

Existence of Multiplicative Identity

Distributive Law

Multiplicative Property

Transitive Property

Trichotomy Property

**Correct answer:**

Trichotomy Property

The real number system, contains order axioms that show relations and properties of the system that add completeness to the ordered field algebraic laws.

The properties are as follows.

Trichotomy Property:

Given , only one of the following statements holds true , , or .

Transitive Property:

For , , and where and then this implies .

Additive Property:

For , , and where and then this implies .

Multiplicative Properties:

For , , and where and then this implies and and then this implies .

Therefore looking at the options the Trichotomy Property identifies the property in this particular question.

### Example Question #2 : Ordered Field And Completeness Axioms

Identify the following property.

For , , and where and then this implies .

**Possible Answers:**

Transitive Property

Multiplicative Properties

Additive Property

Trichotomy Property

Distribution Laws

**Correct answer:**

Transitive Property

The real number system, contains order axioms that show relations and properties of the system that add completeness to the ordered field algebraic laws.

The properties are as follows.

Trichotomy Property:

Given , only one of the following statements holds true , , or .

Transitive Property:

For , , and where and then this implies .

Additive Property:

For , , and where and then this implies .

Multiplicative Properties:

For , , and where and then this implies and and then this implies .

Therefore looking at the options the Transitive Property identifies the property in this particular question.

### Example Question #3 : Ordered Field And Completeness Axioms

Identify the following property.

For , , and where and then this implies .

**Possible Answers:**

Distribution Laws

Trichotomy Property

Transitive Property

Additive Property

Multiplicative Properties

**Correct answer:**

Additive Property

The real number system, contains order axioms that show relations and properties of the system that add completeness to the ordered field algebraic laws.

The properties are as follows.

Trichotomy Property:

Given , only one of the following statements holds true , , or .

Transitive Property:

For , , and where and then this implies .

Additive Property:

For , , and where and then this implies .

Multiplicative Properties:

For , , and where and then this implies and and then this implies .

Therefore looking at the options the Additive Property identifies the property in this particular question.

### Example Question #4 : Ordered Field And Completeness Axioms

Identify the following property.

For , , and where and then this implies and and then this implies .

**Possible Answers:**

Multiplicative Properties

Distribution Laws

Transitive Property

Additive Property

Trichotomy Property

**Correct answer:**

Multiplicative Properties

The properties are as follows.

Trichotomy Property:

Given , only one of the following statements holds true , , or .

Transitive Property:

For , , and where and then this implies .

Additive Property:

For , , and where and then this implies .

Multiplicative Properties:

For , , and where and then this implies and and then this implies .

Therefore looking at the options the Multiplicative Properties identifies the property in this particular question.