Roster Method & Set-Builder Notation...2

[nycmathguy]

College Algebra
Chapter 1/Section 1
Review

We begin our College Algebra journey with a review of the basics according to the author of the textbook.

Working with sets.

There are two methods for denoting sets:

Roster Method
Set-Builder Notation

Here is Sullivan's example.

Let E = set of even digits

Roster Method

E = {0, 2, 4, 6, 8 }

Why did Sullivan include 0 as an element in set E? To me, 0 is not even or odd. You say?

Set-Builder Notation

E = { x| x is an even digit }

You say?

 

[MathLover1]

Numbers that are completely divisible by 2 are termed as even numbers. These numbers when divided by 2 leave 0 as the remainder. For example, 2, 4, 6, 8, and so on.
2 is the smallest even number. It is also the only even prime number.

so, E = {2, 4, 6, 8 }

 

[nycmathguy]

Numbers that are completely divisible by 2 are termed as even numbers. These numbers when divided by 2 leave 0 as the remainder. For example, 2, 4, 6, 8, and so on.
2 is the smallest even number. It is also the only even prime number.

so, E = {2, 4, 6, 8 }

Are you saying that Sullivan made a typo? To me, zero does not belong in set E.

 

[MathLover1]

Sullivan included 0 which could do if includes negative numbers
like set ....-4,-2,0,2,4,...

 

[nycmathguy]

Sullivan included 0 which could do if includes negative numbers
like set ....-4,-2,0,2,4,...

Sullivan would include 0 if E represents the set of positive integers. However, he said E represents the set of even digits. I know that 0 is a digit but it is not even or odd. I think Sullivan made a mistake.

Read what Sullivan said. See screenshot photo.

You say?

 

[MathLover1]

Sullivan did not make mistake.
When 0 is divided by 2, the resulting quotient turns out to also be 0—an integer, thereby classifying it as an even number.

 

[nycmathguy]

Sullivan did not make mistake.
When 0 is divided by 2, the resulting quotient turns out to also be 0—an integer, thereby classifying it as an even number.

I never have been taught that 0/2 = 0 = even digit.
Are you saying that 0/n, where n is any digit is even?
This is so weird.

 

[MathLover1]

yes, 0/n, where n is any digit is even

 

[nycmathguy]

yes, 0/n, where n is any digit is even

Sets are cool.