Union and addition of Intervals

A=[-1,0)

B=(0,1]

Find A U B and A + B (x+y such that x is an element of A and y is an element of B)

I know how to find the answers of two closed intervals but I'm not sure about intervals that are open and closed. Would the answers be considered compact?

Thanks

Re: Union and addition of Intervals

Quote:

Originally Posted by

**willywonk** A=[-1,0) , B=(0,1]

Find A U B and A + B (x+y such that x is an element of A and y is an element of B)

I know how to find the answers of two closed intervals but I'm not sure about intervals that are open and closed. Would the answers be considered compact?

I am not sure exactly notation you are required to use.

$\displaystyle A\cup B=[-1,1]\setminus\{0\}$. WHY?

Edit: I don't understand what happened but part of my reply is missing.

$\displaystyle A+B=(-1,1)$. But you must explain why.

Re: Union and addition of Intervals

I don't know about the **answers** being compact but the sets are not.