All Introduction to Analysis Resources
Example Questions
Example Question #1 :Ordered Field And Completeness Axioms
Identify the following property.
On the spacewhere,only one of the following statements holds true,, or.
Multiplicative Property
Existence of Multiplicative Identity
Transitive Property
三分法的财产
Distributive Law
三分法的财产
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.
三分法的财产:
Given,only one of the following statements holds true,, or.
Transitive Property:
For,, andwhereandthen this implies.
Additive Property:
For,, andwhereandthen this implies.
Multiplicative Properties:
For,, andwhereandthen this impliesandandthen 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,, andwhereandthen this implies.
Distribution Laws
三分法的财产
Additive Property
Multiplicative Properties
Transitive Property
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.
三分法的财产:
Given,only one of the following statements holds true,, or.
Transitive Property:
For,, andwhereandthen this implies.
Additive Property:
For,, andwhereandthen this implies.
Multiplicative Properties:
For,, andwhereandthen this impliesandandthen 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,, andwhereandthen this implies.
Multiplicative Properties
Transitive Property
Additive Property
Distribution Laws
三分法的财产
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.
三分法的财产:
Given,only one of the following statements holds true,, or.
Transitive Property:
For,, andwhereandthen this implies.
Additive Property:
For,, andwhereandthen this implies.
Multiplicative Properties:
For,, andwhereandthen this impliesandandthen 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,, andwhereandthen this impliesandandthen this implies.
Additive Property
Distribution Laws
Multiplicative Properties
三分法的财产
Transitive Property
Multiplicative Properties
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.
三分法的财产:
Given,only one of the following statements holds true,, or.
Transitive Property:
For,, andwhereandthen this implies.
Additive Property:
For,, andwhereandthen this implies.
Multiplicative Properties:
For,, andwhereandthen this impliesandandthen this implies.
Therefore looking at the options the Multiplicative Properties identifies the property in this particular question.