# Building a set notation

1. May 8, 2013

### reenmachine

1. The problem statement, all variables and given/known data

The book I'm reading ask me to build a set notation for the following set: $\{-3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 \}$.

3. The attempt at a solution

I attempted to build a set notation and came with the result:

$\{ x \in R : \exists y\in Z \ \ y(3/4)= x\}$

My idea is that the sequence is always +3/4 or -3/4 , therefore any number in Z multiplied by 3/4 will be an element of the set we're trying to notate.

2. May 8, 2013

### Dick

That's true enough, but the set your notation describes has an infinite number of elements. The original set you wrote down has only 8 elements. Your notation should be a little more specific. Or does the set you are trying to construct also have an infinite number of elements and you only showed 8 of them without a '...'?

3. May 8, 2013

### Fredrik

Staff Emeritus
There's also a way to simplify the notation. Fix the issue that Dick mentioned first, and then try to think of a way to simplify the notation.

4. May 8, 2013

### Dick

I agree. But I think the set reenmachine wants to describe probably has more than 8 elements. I was just trying to clear that up. It's not all that useful to describe small finite sets using set builder notation. Otherwise why not write {x:x∈{−3/2,−3/4,0,3/4,3/2,9/4,3,15/4}}?

5. May 8, 2013

### reenmachine

My apologies for the other thread , thought this one didn't work my computer crashed or something.

I made a mistake , the set I was supposed to find a notation for was the set $\{... , -3/2 , -3/4 , 0 , 3/4 , 3/2 , 9/4 , 3 , 15/4 , ...\}$.

To simplify it , I could try: $\{ n \in Z : n(3/4)\}$ ?

6. May 8, 2013

### Staff: Mentor

It would be {3n/4 : n $\in$ Z}

7. May 8, 2013

### reenmachine

Is there really a difference? If so , is it the left-right factor or is it $3n/4$ versus the $n(3/4)$?

8. May 8, 2013

### Dick

{n∈Z:n(3/4)} doesn't mean anything. What follows the ':' is supposed to be a true/false statement.

9. May 8, 2013

### reenmachine

Ok , in that case , is $\{ n(3/4) : n \in Z\}$ the same as $\{ 3n/4 : n \in Z\}$?

10. May 8, 2013

### Dick

Sure it is. 3n/4=(3/4)n. Isn't it?

11. May 8, 2013

### Staff: Mentor

Yes, but written in a slightly different way. I reversed the order of things in what I wrote for the reason that Dick said.

12. May 8, 2013

### reenmachine

Thanks guys!

So basically , $\{3n/4 : n \in Z\}$ is the shortest way to describe the set with a set notation?

13. May 8, 2013

### Dick

I would say, yes.

14. May 8, 2013

Thanks guys!