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Is the region bounded by a point the entire plane?

Triple integral over a region bounded by surfaces.Are continuous functions with compact support bounded?Find volume of tetrahedron bounded by $x=0$,$y=0$,$z=0$ and the plane $z=1+x-y$.Distance between plane and point.Calculating the volume bounded between a paraboloid and a planeFind the area of the following region D on $xy$-planeHow to determine whether domain is an open or a closed region (or both open and closed)?Finding surface integral of a vector field over quarter of a cylinderFind volume where the region is bounded by $z=1-4(x^2+y^2)$ and the xy plane?Integrating over region bounded by two ellipses

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$begingroup$

Is the region bounded by a point the entire plane? Recently came across this issue in a question - for which the answer implied the affirmative. Can someone elaborate on what the meaning of bounded is? Is there a technical definition?

real-analysis multivariable-calculus

share|cite|improve this question

asked Mar 14 at 6:28

helios321helios321

56149

$endgroup$

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  $begingroup$
  First, to even think of "boundedness", we need a way to find the "distance" between any two points? Do we have it?
  $endgroup$
  – Aniruddha Deshmukh
  Mar 14 at 6:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AniruddhaDeshmukh You going to need to elaborate...
  $endgroup$
  – helios321
  Mar 14 at 8:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The whole notion of boundedness comes from the intuition that a "bounded" set should be one such that the maximum distance between any two points should be finite (or less than some finite quantity). To establish this, we need a way to measure distance between points. Do we have it in this case?
  $endgroup$
  – Aniruddha Deshmukh
  Mar 14 at 9:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There is no way we can have the notion of "boundedness" in terms of "bounded by a point". If you want to have one, you have to define it yourself and see to it that other intuitions do not fail at the same time.
  $endgroup$
  – Aniruddha Deshmukh
  Mar 14 at 9:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AniruddhaDeshmukh Ok then so theres no real "official"position on what to do with a point?
  $endgroup$
  – helios321
  Mar 14 at 12:44
  

  
  
  
  

 | 
show 1 more comment

0

$begingroup$

Is the region bounded by a point the entire plane? Recently came across this issue in a question - for which the answer implied the affirmative. Can someone elaborate on what the meaning of bounded is? Is there a technical definition?

real-analysis multivariable-calculus

share|cite|improve this question

asked Mar 14 at 6:28

helios321helios321

56149

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  First, to even think of "boundedness", we need a way to find the "distance" between any two points? Do we have it?
  $endgroup$
  – Aniruddha Deshmukh
  Mar 14 at 6:50
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AniruddhaDeshmukh You going to need to elaborate...
  $endgroup$
  – helios321
  Mar 14 at 8:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  The whole notion of boundedness comes from the intuition that a "bounded" set should be one such that the maximum distance between any two points should be finite (or less than some finite quantity). To establish this, we need a way to measure distance between points. Do we have it in this case?
  $endgroup$
  – Aniruddha Deshmukh
  Mar 14 at 9:42
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There is no way we can have the notion of "boundedness" in terms of "bounded by a point". If you want to have one, you have to define it yourself and see to it that other intuitions do not fail at the same time.
  $endgroup$
  – Aniruddha Deshmukh
  Mar 14 at 9:43
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @AniruddhaDeshmukh Ok then so theres no real "official"position on what to do with a point?
  $endgroup$
  – helios321
  Mar 14 at 12:44
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

Is the region bounded by a point the entire plane? Recently came across this issue in a question - for which the answer implied the affirmative. Can someone elaborate on what the meaning of bounded is? Is there a technical definition?

real-analysis multivariable-calculus

share|cite|improve this question

asked Mar 14 at 6:28

helios321helios321

56149

$endgroup$

share|cite|improve this question

asked Mar 14 at 6:28

helios321helios321

56149

share|cite|improve this question

asked Mar 14 at 6:28

helios321helios321

56149

asked Mar 14 at 6:28

helios321helios321

56149

asked Mar 14 at 6:28

helios321helios321

56149