What is the set notation for a sequence with a common difference of 3/4?

[reenmachine]

Homework Statement

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 \}##.

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.

Thank you for your help!

 

[Dick]

Homework Statement

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 \}##.

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.

Thank you for your help!

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 '...'?

 

[Fredrik]

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.

 

[Dick]

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.

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}}?

 

[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)\}## ?

 

[Mark44]

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)\}## ?

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

 

[reenmachine]

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

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

 

[Dick]

Is there really a difference?

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

 

[reenmachine]

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

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

 

[Dick]

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

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

 

[Mark44]

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

 

[reenmachine]

Thanks guys!

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

 

[Dick]

Thanks guys!

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

I would say, yes.

 

[reenmachine]

Thanks guys!