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{x: \frac{1}{2}\ < |x| < 1}

First, let us talk about what an open set will look like.

Every open set in \(\mathbb{R}\) can be written as the union of intervals of the form \((a, b)\).

please wait let me think

yes , it can be written like that

Show me.

\[(-1,1/2) \cup(1/2,1)\]

so that the union =(-1,1)

yes but please explain this
\[[−1,1]∩[(−1,−1/2)∪(1/2/1)] \]

i know that [−1,1]∩[(−1,−1/2)∪(1/2,1)] is open in R

but i know that [-1,1] is close in R.

I really think if you ask about one of the other options, this one will make more sense...

ok but do you have any examples to make me understand more?

and \(\{x\mid \frac{1}{2}< |x| \le 1\}\)
and \(\{x\mid \frac{1}{2}\le |x| \le 1\}\)

You here man? These are yes or no questions :)

YES THEY DID.

NETWORK IS TOOOOOO POOR

OK, NOW it means that the option that is close is \[{{x∣1/2≤|x|≤1} } \] is the close set. ?

Which one would you like to look at?

\[{x∣1/2<|x|≤1} \] this one first, is it open or close in R . i guess it is neither

Try and write that set as the union of open intervals.

will it be \[(-1,-\frac{ 1 }{ 2})\cup(\frac{ 1 }{ 2 },1]\]

am i right sir?

which book or site can i lean how to do this sir?

i thick it can not be written

\([-1,-\frac{ 1 }{ 2})\cup(\frac{ 1 }{ 2 },1]\)

The book I gave you covers this in detail.

Answer this please
\([(-2,\dfrac{-1}{2})\cup(\dfrac{1}{2},2)]\cap[-1,1]= \ ?\)

Just answer the last question I asked

the answer to that question you asked is (-1,1)

i have not studied sub base sir

i am confuse

at first i thought the answer to that your question is empty set but i was not sure

I am not trying to be rude, but it is a waste of time.

thank you sir

we are talking about the first question.

or at least I am.

ohh. i thought we have answered the first question

Ok Close this and ask the new question :)