A Quick Question on Valid Set Builder Notation

Hello; today my Precalculus teacher gave this definition for the set of rational numbers:

$\displaystyle Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}$

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:

$\displaystyle Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}$

or

$\displaystyle Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}$?

Thanks,

yottaflop

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:

$\displaystyle Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}$

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:

$\displaystyle Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}$

or

$\displaystyle Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}$?

Thanks,

yottaflop

Your Precalculus teacher is wrong!

$\displaystyle \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

Re: A Quick Question on Valid Set Builder Notation

Hello, yottaflop!

A few spaces will provode clarity.

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

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

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

If it does, it may bring back public flogging.

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.

Re: A Quick Question on Valid Set Builder Notation

Quote:

Originally Posted by

**Soroban** Hello, yottaflop!

A few spaces will provode clarity.

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

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

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

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...

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:

$\displaystyle Q= \{ r|r= \frac{a}{b} ,a,b \in Z,b \not =0 \}$

=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:

$\displaystyle Q= \{ r|r= \frac{a}{b} , \{a,b \} \in Z,b \not =0 \}$

or

$\displaystyle Q= \{ r|r= \frac{a}{b} ;a,b \in Z,b \not =0 \}$?

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!