## UnkleRhaukus Group Title $(1,2)\cap[2,3)=$ @estudier 2 years ago 2 years ago

1. UnkleRhaukus

can you confirm the solution is the empty set?

2. estudier

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

3. ParthKohli

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.

4. estudier

They are not really sets....

5. ParthKohli

They are. :p

6. UnkleRhaukus

intervals

7. ParthKohli

Intervals are sets.

8. UnkleRhaukus

an interval in set on an infinite number of points

9. estudier

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

10. ParthKohli

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

11. estudier

Maybe, it wasn't actually defined...

12. UnkleRhaukus

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

13. ParthKohli

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

14. Zarkon

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

15. ParthKohli

Yes, the set builder notation.

16. UnkleRhaukus

yeah

17. UnkleRhaukus

thats what i ment @Zarkon

18. ParthKohli

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

19. UnkleRhaukus

what is phi?

20. ParthKohli

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

21. ParthKohli

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

22. UnkleRhaukus

strange choice of dummy variable

23. ParthKohli

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

24. UnkleRhaukus

i did not know that

25. UnkleRhaukus

so i was right? $(1,2)\cap[2,3)=\emptyset$

26. ParthKohli

It's actually in Eurasia - Europe.

27. ParthKohli

28. UnkleRhaukus

not you

29. ParthKohli

I wasn't right? I was.

30. estudier

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

31. UnkleRhaukus

you dont know which way is east parth

32. ParthKohli

Eastern Hemisphere. Okay?

33. UnkleRhaukus

ok

34. UnkleRhaukus

thanks all,

35. ParthKohli

You're welcome.