Hello. I’m Professor Von Schmohawk

and welcome to Why U. In the previous lecture we saw how to create

a binary relation between two sets. These sets can contain any type of elements. We showed that a binary relation is a way of associating or relating elements

of one set to elements of the other set. For instance, we could draw arrows

from each person in set A who likes fruit to the fruits in set B which they like. As we saw, this same information can be conveyed

using ordered pairs where the first element of each ordered pair

is a member of the first set and the second element

is a member of the second set. Let’s name a set containing these

ordered pairs, set L. So L represents a binary relation

from A to B. In a binary relation not every element in the two sets which are

related may be involved in the relation. In our example, Tarzan, Boy, oranges, apples,

and bananas are part of relation L while Jane, pears, and cherries are not. The set of all elements of A

which are L-related to elements of B is called the “domain” of L. Likewise, the set of all elements of B

to which the elements of A are related is called the “range” of L. So in a binary relation from A to B all the elements of A which are related

form the domain and all the elements of B which are related

form the range. The domain and range

are subsets of A and B. The domain and the range can include

every element of A and B or could include just a single element. We have illustrated binary relations, between

sets containing various types of elements. But often in Algebra

the sets which are related are both equal to the

set of real numbers R. In this case, we can either say that

the binary relation is from R to R or more simply

that the binary relation is “on” R. The ordered pairs which represent a binary

relation on R are pairs of real numbers. This set of ordered pairs is sometimes referred

to as the “graph” of the relation. And since Cartesian coordinates can be used to visually represent ordered pairs

of real numbers this is a way to visually represent

the graph of a relation on R. Creating this visual representation of a relation

is called “graphing” the relation and is one of the most powerful methods

for understanding mathematical relations. There are many types of graphs. Graphs of finite sets of ordered pairs

like this are called “scatter plots”. In the next lecture, we will see how

scatter plots can be an important tool allowing us to visually recognize patterns

which may exist in a binary relation.

## 10 Comments

## aljosf

i just came back to see if you added a new vid, and it was today, i think you guys are doing an amazing job of conveying ideas, bravo! Seriously!

## Francis Guiller Santos

I want a video about complex numbers!

## Pedro Alonso Cazorla Saravia

Is there a name given to the set A regardless if is equal or not to the domain of the relation?

## shaahkar siddiquee

Things that would baffle me for years, thanks to Professor Von Schmohawk AND the team, I learned and grasped in days. There is something very very right about Why U. Thanks Guys.

## Pedro Alonso Cazorla Saravia

Wikipedia:

Partial function from X to Y: ƒ: X' → Y, where X' is a subset of X

"There are two distinct meanings in current mathematical usage for the notion of the domain of a partial function. Most mathematicians, including recursion theorists, use the term "domain of f" for the set of all values x such that f(x) is defined ( X' above). But some, particularly category theorists, consider the domain of a partial function f:X→Y to be X, and refer to X' as the domain of definition."

## Yoshi Fujimoto

Another great video. Thanks again!

## John Brasely

awesomeeeeeeeeeeeeee

## Hasnain Farid

best explanation

## omarder channel

Your extremly talanted please continue

## Jazz Day

Another great video! THANKS