Sets: Given ? = {? ∈ ℤ|1 ≤ ? ≤ ?0}, define ?? = {? ∈ ?|? ?? factor of ?}

Sets: Given ? = {? ∈ ℤ|1 ≤ ? ≤ ?0}, define ?? = {? ∈ ?|? ?? factor of ?}

Hi,

can someone help me with understanding this:

Let ? = {? ∈ ℤ|1 ≤ ? ≤ ?0}.
For any positive integer ? we define the set ?? by?? = {? ∈ ?|? ?? factor of ?}

So I created set A = {-infinite,...,-1,0,1,2,...,10}
But I'm stuck with Am.

Is this right solution?

A1 = {1}
A2 = {1,2}
A3 = {1,2,3}
...
?
Thanks

kironet said:

Let ? = {? ∈ ℤ|1 ≤ ? ≤ ?0}.
For any positive integer ? we define the set ?? by?? = {? ∈ ?|? ?? factor of ?}

So I created set A = {-infinite,...,-1,0,1,2,...,10}
But I'm stuck with Am.

Is this right solution?

A1 = {1}
A2 = {1,2}
A3 = {1,2,3}
...
?

Click to expand...

I dunno. What did they tell you to do with "A" and "Am"? Are you supposed to list out the elements of all such sets "Am"? Or something else?

Thank you!

kironet said:

Hi,

can someone help me with understanding this:

Let ? = {? ∈ ℤ|1 ≤ ? ≤ ?0}.
For any positive integer ? we define the set ?? by?? = {? ∈ ?|? ?? factor of ?}

So I created set A = {-infinite,...,-1,0,1,2,...,10}
But I'm stuck with Am.

Is this right solution?

A1 = {1}
A2 = {1,2}
A3 = {1,2,3}
...
?
Thanks

Click to expand...

Your "A" is wrong; you seem to have missed that 1 ≤ n.

If you were told to write out the first several sets A_m, when you say that A₃ = {1,2,3}, you are saying that 1, 2, and 3 are all factors of 3 (since m is 3, and you need to list every element of A that is a factor of m). Is that right?

Hi, sorry this is the full question:

Let ? = {? ∈ ℤ|1 ≤ ? ≤ ?0}.
For any positive integer ? we define the set ?? by?? = {? ∈ ?|? ?? factor of ?}

Give the sets ?3, ?6 and ?8 explicitly in terms of their elements.

After research I came up with this:

A = {1,2,...,10}
A3={1,3}
A6={1,2,3,6}
A8={1,2,4,8}

Does it look correct?

kironet said:

Hi, sorry this is the full question:

Let ? = {? ∈ ℤ|1 ≤ ? ≤ ?0}.
For any positive integer ? we define the set ?? by?? = {? ∈ ?|? ?? factor of ?}

Give the sets ?3, ?6 and ?8 explicitly in terms of their elements.

After research I came up with this:

A = {1,2,...,10}
A3={1,3}
A6={1,2,3,6}
A8={1,2,4,8}

Does it look correct?

Click to expand...

Well, let's check it:

A = {1,2,...,10} -- these are the numbers such that 1 ≤ ? ≤ ?0 -- yes
A3={1,3} -- these are the numbers in A such that each is a factor of 3 -- yes
A6={1,2,3,6} -- these are the numbers in A such that each is a factor of 6 -- yes
A8={1,2,4,8} -- these are the numbers in A such that each is a factor of 8 -- yes

Good job!

I find it helpful to think of the condition in "set builder notation" as a test that an entity has to pass in order to be allowed into the set -- a membership exam, if you like. So we give each element that test (and make sure that no one else would pass it), and we see that your answer is right.