Question

\[(1,2)\cap[2,3)=\] @estudier

Answer 1

can you confirm the solution is the empty set?

Answer 2

2 included in 1 and not the other so nothing in common.

Answer 3

An arbitrary element \(\phi\) will always fulfil the condition \(\phi <2\) in set \((1,2)\).
An arbitrary element \(\psi\) will always fulfil the condition \(\psi \ge 2 \) in set \([2,3)\).

So, \(\rm \psi \ge 2>\phi\).

Therefore, there is no common element.

Answer 4

They are not really sets....

Answer 5

They are. :p

Answer 6

intervals

Answer 7

Intervals are sets.

Answer 8

an interval in set on an infinite number of points

Answer 9

@ParthKohli (1,2) What set is this?

Answer 10

{1.000000000000.....1, 1.000000......2 ..... 1.99999999999999........9}

Answer 11

Maybe, it wasn't actually defined...

Answer 12

\[x\in\mathbb R[1<x<2)]\]

Answer 13

The interval (1,2) can be interpreted as a set containing numbers between and not including 1 and 2.

Answer 14

\[(1,2)=\{x\in\mathbb{R}|1<x<2\}\]

Answer 15

Yes, the set builder notation.

Answer 16

yeah

Answer 17

thats what i ment @Zarkon

Answer 18

In this case, we have \(\phi \) instead.\[(1,2) = \{\phi \in \mathbb R |1<\phi <2\}\]Doesn't make a lot of difference either...

Answer 19

what is phi?

Answer 20

An arbitrary element in \((1,2)\).

Answer 21

Or if you're asking it that way, phi is a Greek letter.

Answer 22

strange choice of dummy variable

Answer 23

Greece is a country located in the east, precisely the Asian continent.

Answer 24

i did not know that

Answer 25

so i was right?

\[(1,2)\cap[2,3)=\emptyset\]

Answer 26

It's actually in Eurasia - Europe.

Answer 27

Yes, my lad.

Answer 28

not you

Answer 29

I wasn't right? I was.

Answer 30

I said u were right back on the second post...

Answer 31

you dont know which way is east parth

Answer 32

Eastern Hemisphere. Okay?

Answer 33

ok

Answer 34

thanks all,

Answer 35

You're welcome.