Order theory | Type theory | Basic concepts in set theory
In mathematics, an ordered pair (a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.) Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional vectors. (Technically, this is an abuse of terminology since an ordered pair need not be an element of a vector space.)The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects). For example, the ordered triple (a,b,c) can be defined as (a, (b,c)), i.e., as one pair nested in another. In the ordered pair (a, b), the object a is called the first entry, and the object b the second entry of the pair. Alternatively, the objects are called the first and second components, the first and second coordinates, or the left and right projections of the ordered pair. Cartesian products and binary relations (and hence functions) are defined in terms of ordered pairs, cf. picture. (Wikipedia).
This video answers two questions: What are ordered pairs? How do you graph them?
From playlist Algebra
Determine If an Ordered Pair is a Solution to a Linear Equation
This video explains how to determine if an ordered pair is a solution to a given linear equation. http://mathispower4u.com
From playlist Graphing Linear Equations Using a Table of Values
Ex: Determine If An Ordered Pair is a Solution to a Linear Equation
This video explains how to determine in a given ordered pair is a solution to a linear equation. http://mathispower4u.com
From playlist Graphing Linear Equations Using a Table of Values
From playlist 2. Attributes of Functions
Set Theory (Part 3): Ordered Pairs and Cartesian Products
Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser
From playlist Set Theory by Mathoma
Ex: Determine One Value of An Ordered Pair to Satisfy a Linear Equation (Fractions)
This video explains how to determine a missing value of an ordered pair to make the ordered pair a solution to a linear equation. http://mathispower4u.com
From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables
Use a Graph Determine Ordered Pair Solutions of a Linear Inequality in Two Variable
This video explains how to select ordered pair solutions from the graph of a linear inequality of two variables. mathispower4u.com
From playlist Solving Linear Inequalities in Two Variables
The elements of a set can be ordered by a relation. Some relation cause proper ordering and some, partial ordering. Have a look at some examples.
From playlist Abstract algebra
Ordered Pair Solutions to Linear Inequalities of Two Variables
This video explains how to check to see if an ordered pair is a solution to a linear inequality in two variables.
From playlist Solving Linear Inequalities in Two Variables
Orders on Sets: Part 2 - Total Orders
This was recorded as supplemental content for Math 115AH in the spring quarter of 2020. In this video, we investigate in detail a simple example of a poset, and define a new notion: "total order". Hold music: Bossa Antigua by Kevin MacLeod Link: https://incompetech.filmmusic.io/song/3454
From playlist Orders on Sets
Verifying Ordered Pairs Satisfy a Linear Equation in Two Variables (L8.3)
This video explains how to verify given ordered pairs satisfy a linear equation. The results are verified by graphing the points. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables
Determine if Ordered Pairs are Solutions to a Quadratic Equation
This video explains how to determine if given ordered pairs are solution to a given question in two variables. http://mathispower4u.com
From playlist Solving Quadratic Equations by Factoring
Introduction to Linear Inequalities in Two Variables (L11.6)
This lesson introduces linear inequalities in two variables. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Solving Linear Inequalities in Two Variables
Determine if Ordered Pairs are Solutions to a Absolute Value Equation
This video explains how to determine if given ordered pairs are solution to a given question in two variables. http://mathispower4u.com
From playlist Solving Absolute Value Equations
Introduction to Relations and Functions
An introduction to relations and functions. Discussion includes defining, classifying, and examples of relations and functions, as well as five ways to represent relations and functions,
From playlist Algebra 1
Ex: Determine if Ordered Pairs Satisify a Linear Inequality in Two Variables (09x-42)
This video explains how to determine if an ordered pair satisfies a linear inequality in two variable. The results are verified graphically.
From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables
Determine if Ordered Pairs are Solutions to a Linear Equation (y=mx+b)
This video explains how to determine if given ordered pairs are solution to a given question in two variables. http://mathispower4u.com
From playlist Graphing Linear Equations Using a Table of Values
Determine if an Ordered Pair is a Solution to a System of Linear Equations
This video explains how to determine if an ordered pair is a solution to a system of linear equations. http://mathispower4u.com
From playlist Solving Systems of Linear Inequalities