anonymous
  • anonymous
What is open set, close set , neighborhood , bound , compact , and connected? Let S={(x,y): -1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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experimentX
  • experimentX
looks like open set ... -1<=x<=1, is a closed set, in both cases bound is -1 (greatest lower bound) and +1(smallest upper bound), all values beyond GLB and SUB is also a bound ..... if the set has finite number of sub cover ... it's called compact ==> that's all i studied ... but never understood clearly.
anonymous
  • anonymous
Dint understand anything :-( I looked for this ques 's ans , and its written dt its neither open nor closed :-((
anonymous
  • anonymous
If your set is in the plane. Then it is clearly bounded. It is not open since it cannot contains any disc. It is not closed. because \[x_n=1-\frac 1 n\] is a sequence in it that tens to 1 and 1 is not in the set. So it is not compact.

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anonymous
  • anonymous
tends
anonymous
  • anonymous
I dont know anything about sequence , some odr way to explain plz ?
anonymous
  • anonymous
Do some reading about it.
anonymous
  • anonymous
See I have the ans but not able to understand , here it goes : Its not open because a set of Z integers is nt open set , its not closed because R square -S is not open as (-1,0) has no disc centred at (-1,0) and contained in Rsquare - S ! now wt does ds mean ?
experimentX
  • experimentX
i myself seems not to understand it ... lol
anonymous
  • anonymous
yea its toooo tiring ! since morning ( in india ) , Iam doing ol ds stufff , bt no progress ! :<<<
anonymous
  • anonymous
Do some reading about open, closed sets in the plane.
experimentX
  • experimentX
|dw:1333609817243:dw|
anonymous
  • anonymous
nothing getn in my head , just off my head fr sure ! :p
anonymous
  • anonymous
\( S=\{(x,y): -1
anonymous
  • anonymous
ds is d ques , @ FFM , cnt hlp it ! :p
anonymous
  • anonymous
An open set in the plane is a set O, such that if x is in O, then there is a disk centered at x and contained in O. A set is closed if the complement of it is open. A set D is bounded, if there is a constant k such that for every z in K, |z| < k
anonymous
  • anonymous
It's \( y =o \) o or 0?
anonymous
  • anonymous
But I don't understand what do you mean by y=o ? It is the interval (-1,1) in the plane {(x,0}, -1 < x < 1}
TuringTest
  • TuringTest
I don't know about sets, but I know about regions a bit. A region is closed if it contains its boundary since we have < and not \(\le\), the endpoints are not included it is bounded if the region can be contained in a disk, which experimentX has shown it can be I don't know what compact is...
anonymous
  • anonymous
First i will run all the options using set -1
anonymous
  • anonymous
@anjali_pant
anonymous
  • anonymous
In case of S={(x,y): -1
anonymous
  • anonymous
@anjali_pant
anonymous
  • anonymous
was it helpfull?
anonymous
  • anonymous
in d case of limit points , how do we knw dt its nt contained ?
anonymous
  • anonymous
@myko: So you think \( y=o \) makes any sense?!!!
anonymous
  • anonymous
yup ofcourse @ FFM
anonymous
  • anonymous
A limit point is a point that has infinitly many point's of the set in any of his neghborhoods. All points of-1
anonymous
  • anonymous
so it can't be closed
anonymous
  • anonymous
It should not, it does not. But if you make \( y=0 \) then probably somewhat.
anonymous
  • anonymous
how do we knw dt ?
anonymous
  • anonymous
@myko
anonymous
  • anonymous
dt?
anonymous
  • anonymous
that -> dt lol
anonymous
  • anonymous
dt its not included ?
anonymous
  • anonymous
becouse it says -1
anonymous
  • anonymous
oh yea ! my fault , stupid ques ! :P
anonymous
  • anonymous
Btw closed set: set that contains all it's limit points -1
anonymous
  • anonymous
okie I have another similar query ! S={(x,y) : x=0 or y=0 }
anonymous
  • anonymous
No the question is not that stupid lol.
anonymous
  • anonymous
it is
anonymous
  • anonymous
read my first answer
anonymous
  • anonymous
in this topic
anonymous
  • anonymous
S={(x,y) : x=0 or y=0 } its a set that is bouth x and y axis of the real line
anonymous
  • anonymous
|dw:1333612387695:dw| only lines belong to the set
anonymous
  • anonymous
hey in my previous ques , did u say dt its open ?
anonymous
  • anonymous
i still don't get it. What dt is?
anonymous
  • anonymous
dt means that, she is using sms lingo ;)
anonymous
  • anonymous
ya, i guessed that already
anonymous
  • anonymous
In my previous query , did u say dt S is open ?
anonymous
  • anonymous
:)
anonymous
  • anonymous
dt?????????????????????????????
anonymous
  • anonymous
Wherever you see dt replace it by "that" and it has nothing to do with derivative lol
anonymous
  • anonymous
lol my fault
anonymous
  • anonymous
s in previous question is not open in (x,y)
anonymous
  • anonymous
okay time for lunch. See you guys later.
anonymous
  • anonymous
it would be open in R
anonymous
  • anonymous
c ya
anonymous
  • anonymous
any more queations?
anonymous
  • anonymous
n wt abt ds ques ? cya @FFm , please explain ! @myko

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