# A Quick Question on Valid Set Builder Notation

• Jul 5th 2011, 09:15 AM
yottaflop
A Quick Question on Valid Set Builder Notation
Hello; today my Precalculus teacher gave this definition for the set of rational numbers:
$Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}$
Couldn't this be interpreted to mean that r equals both a/b and a, that b belongs to Z (the set of integers), and that b is not equal to zero?
Shouldn't it be:
$Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}$
or
$Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}$?
Thanks,
yottaflop
• Jul 5th 2011, 10:07 AM
Also sprach Zarathustra
Re: A Quick Question on Valid Set Builder Notation
Quote:

Originally Posted by yottaflop
Hello; today my Precalculus teacher gave this definition for the set of real numbers:
$Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}$
Couldn't this be interpreted to mean that r equals both a/b and a, that b belongs to Z (the set of integers), and that b is not equal to zero?
Shouldn't it be:
$Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}$
or
$Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}$?
Thanks,
yottaflop

$\mathbb{Q}$ is set of all rational numbers.

Here you can find some information:

Real number - Wikipedia, the free encyclopedia

Rational number - Wikipedia, the free encyclopedia
• Jul 5th 2011, 12:00 PM
Soroban
Re: A Quick Question on Valid Set Builder Notation
Hello, yottaflop!

A few spaces will provode clarity.

. . $Q \:=\: \{ r\,|\,r= \tfrac{a}{b},\;a,b \in Z,\;b \ne 0 \}$

I seriously doubt that a textbook would write it like this:

. . $Q\!=\!\{r|r\!=\!\tfrac{a}{b},\!a,\!b\!\in\!Z,\!b\! \ne\!0\}$

If it does, it may bring back public flogging.

• Jul 5th 2011, 02:13 PM
yottaflop
Re: A Quick Question on Valid Set Builder Notation
Thank you both; Also sprach: that was a typo on my part, sorry for the confusion. I've edited my original post to fix it.
• Jul 6th 2011, 06:48 PM
skoker
Re: A Quick Question on Valid Set Builder Notation
Quote:

Originally Posted by Soroban
Hello, yottaflop!

A few spaces will provode clarity.

. . $Q \:=\: \{ r\,|\,r= \tfrac{a}{b},\;a,b \in Z,\;b \ne 0 \}$

I seriously doubt that a textbook would write it like this:

. . $Q\!=\!\{r|r\!=\!\tfrac{a}{b},\!a,\!b\!\in\!Z,\!b\! \ne\!0\}$

If it does, it may bring back public flogging.

I will direct you to this scrappy pack of textbook editors that have decided monkeys para-shooting out of planes and tightrope walking clowns will 'help' explain the math...
• Jul 7th 2011, 01:10 PM
HallsofIvy
Re: A Quick Question on Valid Set Builder Notation
Quote:

Originally Posted by yottaflop
Hello; today my Precalculus teacher gave this definition for the set of rational numbers:
$Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}$
=Couldn't this be interpreted to mean that r equals both a/b and a, that b belongs to Z (the set of integers), and that b is not equal to zero?
Shouldn't it be:
$Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}$
or
$Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}$?
Thanks,
yottaflop

The second is better than what you initially give. The first of your suggestions is definitely wrong since it is requiring that the set, {a, b}, be an integer!