Expert: Paul Klarreich - 1/31/2009

Question
QUESTION: How would you write "The set of all calculus books" in set-builder notation?

Is it {x|x is a calculus book} or {x is a calculus book}?

ANSWER: Questioner:   Jenny
Category:  Calculus
Private:  No
 
Subject:  Set-builder Notation
Question:  How would you write "The set of all calculus books" in set-builder notation?

Is it {x|x is a calculus book} or {x is a calculus book}?
.............................  

Hi, Jenny,

I like the first one.  Even better might be:

{ x  in {books} |  x does calculus }

but that is getting too pedantic.

The first is fine.


---------- FOLLOW-UP ----------

QUESTION: Thank you so much!

Also...
Find the number of proper subsets of the set.

{x|x is a day of the week}

Is the answer:

128
127
256
64

Thank you in advance.

Answer
Questioner:   Jenny
Category:  Calculus
Private:  No
 
Subject:  Set-builder Notation
Question:  QUESTION: How would you write "The set of all calculus books" in set-builder notation?

Is it {x|x is a calculus book} or {x is a calculus book}?

ANSWER: Questioner:   Jenny
Category:  Calculus
Private:  No

Subject:  Set-builder Notation
Question:  How would you write "The set of all calculus books" in set-builder notation?

Is it {x|x is a calculus book} or {x is a calculus book}?
.............................  

Hi, Jenny,

I like the first one.  Even better might be:

{ x  in {books} |  x does calculus }

but that is getting too pedantic.

The first is fine.


---------- FOLLOW-UP ----------

QUESTION: Thank you so much!

Also...
Find the number of proper subsets of the set.

D = {x|x is a day of the week}

Is the answer:

128
127
256
64

Thank you in advance.
............................
Hi, Jenny,

Your set D is { Sun,Mon,Tue,..,Sat } and has 7 elements.  Such a set always has 2^7 = 128 subsets.

Proper subsets?  It means subsets EXCEPT D itself, so that would mean 127, right?