UnkleRhaukus
\[(1,2)\cap[2,3)=\] @estudier
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UnkleRhaukus
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can you confirm the solution is the empty set?
estudier
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2 included in 1 and not the other so nothing in common.
ParthKohli
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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.
estudier
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They are not really sets....
ParthKohli
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They are. :p
UnkleRhaukus
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intervals
ParthKohli
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Intervals are sets.
UnkleRhaukus
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an interval in set on an infinite number of points
estudier
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@ParthKohli (1,2) What set is this?
ParthKohli
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{1.000000000000.....1, 1.000000......2 ..... 1.99999999999999........9}
estudier
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Maybe, it wasn't actually defined...
UnkleRhaukus
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\[x\in\mathbb R[1<x<2)]\]
ParthKohli
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The interval (1,2) can be interpreted as a set containing numbers between and not including 1 and 2.
Zarkon
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\[(1,2)=\{x\in\mathbb{R}|1<x<2\}\]
ParthKohli
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Yes, the set builder notation.
UnkleRhaukus
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yeah
UnkleRhaukus
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thats what i ment @Zarkon
ParthKohli
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In this case, we have \(\phi \) instead.\[(1,2) = \{\phi \in \mathbb R |1<\phi <2\}\]Doesn't make a lot of difference either...
UnkleRhaukus
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what is phi?
ParthKohli
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An arbitrary element in \((1,2)\).
ParthKohli
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Or if you're asking it that way, phi is a Greek letter.
UnkleRhaukus
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strange choice of dummy variable
ParthKohli
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Greece is a country located in the east, precisely the Asian continent.
UnkleRhaukus
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i did not know that
UnkleRhaukus
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so i was right?
\[(1,2)\cap[2,3)=\emptyset\]
ParthKohli
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It's actually in Eurasia - Europe.
ParthKohli
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Yes, my lad.
UnkleRhaukus
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not you
ParthKohli
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I wasn't right? I was.
estudier
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I said u were right back on the second post...
UnkleRhaukus
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you dont know which way is east parth
ParthKohli
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Eastern Hemisphere. Okay?
UnkleRhaukus
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ok
UnkleRhaukus
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thanks all,
ParthKohli
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You're welcome.