Please check/confirm if the set is correct

[Math100]

Homework Statement

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

Relevant Equations

None.

Can anyone please check/confirm if the set is correct? I've boxed around my answer.

 

[fresh_42]

Homework Statement:: Write each of the following sets by listing their elements between braces.
Relevant Equations:: None.

Can anyone please check/confirm if the set is correct? I've boxed around my answer.

Almost. What about $x=\pm 4$?

 

[Math100]

Almost. What about $x=\pm 4$?

Oh, yes! You just reminded me something. I am so sorry, I forgot that this is a closed interval where both 4 and -4 are included in the set.

 

[Math100]

How about this time? Is it correct?

 

[fresh_42]

How about this time? Is it correct?

That's ok. You could write it in the following way if you want to be precise:
\begin{align*}
\{5x\,|\,x\in \mathbb{Z}\wedge |2x|\leq 8\}&=5\cdot \{x\in \mathbb{Z}\,|\,2\cdot |x|\leq 8\}=5\cdot \{x\in \mathbb{Z}\,|\, |x|\leq 4\}\\&=5\cdot \{x\in \mathbb{Z}\,|\, -4\leq x\leq 4\}=5\cdot\{-4,-3,-2,-1,0,1,2,3,4\}\\
&=\{-20,-15,-10,-5,0,5,10,15,20\}
\end{align*}

(edited to make it shorter)

 

[Math100]

That's ok. You could write it in the following way if you want to be precise:
\begin{align*}
\{5x\,|\,x\in \mathbb{Z}\wedge |2x|\leq 8\}&=5\cdot \{x\in \mathbb{Z}\,|\,2\cdot |x|\leq 8\}=5\cdot \{x\in \mathbb{Z}\,|\, |x|\leq 4\}\\&=5\cdot \{x\in \mathbb{Z}\,|\, -4\leq x\leq 4\}=5\cdot\{-4,-3,-2,-1,0,1,2,3,4\}\\
&=\{-20,-15,-10,-5,0,5,10,15,20\}
\end{align*}

(edited to make it shorter)

Thank you so much for this! I think this is much more precise and professional! I've never seen this before!

 

[Mark44]

As a minor point, whatever follows "therefore" should be a statement, such as an equality or inequality, not just an expression, such as {-4, -3, -2, -1, 0, 1, 2, 3, 4}.

Following @fresh_42's work, you could conclude something like this:
Therefore, $\{5x\,|\,x\in \mathbb{Z}\wedge |2x|\leq 8\} =\{-20,-15,-10,-5,0,5,10,15,20\}$

 

[Math100]

As a minor point, whatever follows "therefore" should be a statement, such as an equality or inequality, not just an expression, such as {-4, -3, -2, -1, 0, 1, 2, 3, 4}.

Following @fresh_42's work, you could conclude something like this:
Therefore, $\{5x\,|\,x\in \mathbb{Z}\wedge |2x|\leq 8\} =\{-20,-15,-10,-5,0,5,10,15,20\}$

Thank you for pointing that out, I will keep that in mind.