Set builder notation question.

[Jim01]

Homework Statement

Use the set-roster notation to indicate the elements in each of the following sets.

Homework Equations

S = {n ∈Z |n(-1)k, for some integer k}

The Attempt at a Solution

Here is how I read this:

"S is the set of all n’s that are a member of the integers, such that n=(-1)k for some integer k."

I am confused about how to go about indicating the elements in this set. Specifically, how does k fit into the picture? If k can be any integer, then would n not also be any integer? Changing k would change n wouldn't it? If this is true then wouldn't the elements be all integers?

 

[Mark44]

Homework Statement

Use the set-roster notation to indicate the elements in each of the following sets.

Homework Equations

S = {n ∈Z |n(-1)k, for some integer k}

From what you have below, this description should say n = (-1)k. IOW, you have omitted the equal sign.

The Attempt at a Solution

Here is how I read this:

"S is the set of all n’s that are a member of the integers, such that n=(-1)k for some integer k."

I am confused about how to go about indicating the elements in this set. Specifically, how does k fit into the picture? If k can be any integer, then would n not also be any integer? Changing k would change n wouldn't it? If this is true then wouldn't the elements be all integers?

If I understand what you have described, S is the set of all integers. If k is an integer, then -k is in S. Here k can be negative or positive (or zero). No matter which integer you take for k, such as 3, -5, or 0, -k (equallying, respectively, -3, -(-5) = 5, or 0) is still an integer.