Finding the elements of these sets

[Math100]

Homework Statement

Write each of the following sets by listing their elements between braces.

Relevant Equations

None.

Can anyone please check/confirm my answers? I've shown my work and I boxed around all of my answers. Thank you.

 

[FactChecker]

It's good except the last one, where you should specify what values n can take.

 

[Math100]

It's good except the last one, where you should specify what values n can take.

But how should I specify what values n can take? Any hints?

 

[Mark44]

But how should I specify what values n can take? Any hints?

Can n be an arbitrary rational number, such as 1/2? Can n be any real number? Some details on the possible values of n are what @FactChecker is looking for.

 

[Math100]

No, n cannot be 1/2.

 

[FactChecker]

Just say what set of values n can take. Like {$2\pi n, n \in ?$}

 

[Math100]

Just say what set of values n can take. Like {##2\pi n, n \in ?

{...,-4pi, -2pi, 0, 2pi, 4pi, ...}

 

[Mark44]

{...,-4pi, -2pi, 0, 2pi, 4pi, ...}

So for $2\pi n$ to take on those values, what set of numbers does n belong to? That's what we're trying to get you to tell us.

 

[Math100]

So for $2\pi n$ to take on those values, what set of numbers does n belong to? That's what we're trying to get you to tell us.

{..., -2, -1, 0, 1, 2, ...}
Is that the right answer?

 

[FactChecker]

{..., -2, -1, 0, 1, 2, ...}
Is that the right answer?

Also known as the integers, $\mathbb{Z}$
So a good expression of the answer is {$2\pi n, n \in \mathbb{Z}$}

 

[Math100]

Also known as the integers, $\mathbb{Z}$
So a good expression of the answer is {$2\pi n, n \in \mathbb{Z}$}

Thank you so much!