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

[kironet]

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

 

[stapel]

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}
...
?

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!

 

[Dr.Peterson]

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

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?

 

[kironet]

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?

 

[Dr.Peterson]

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?

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.