please answer my question
I am waiting for answer since 3 years
Answers
Case 1
Assume that there is no black point which is at a dist of one unit from a white pt
Assume that there is no black point which is at a dist of one unit from a white ptPick a black pt and make a circle of radius 1 around it
Assume that there is no black point which is at a dist of one unit from a white ptPick a black pt and make a circle of radius 1 around itFrom our assumption, it's trivial to say that all the points on the circle will also be blackk
Assume that there is no black point which is at a dist of one unit from a white ptPick a black pt and make a circle of radius 1 around itFrom our assumption, it's trivial to say that all the points on the circle will also be blackkEvery point inside the circle will have one point on the circumference which Is at a distance of one unit from it. So all the points inside have to be black as well
Assume that there is no black point which is at a dist of one unit from a white ptPick a black pt and make a circle of radius 1 around itFrom our assumption, it's trivial to say that all the points on the circle will also be blackkEvery point inside the circle will have one point on the circumference which Is at a distance of one unit from it. So all the points inside have to be black as wellSo essentially you have a black circular patch. You can pick another point on this circle as the centre and repeat the same process. You'll end up with a plane filled with all black points and 0 white points, which Is a contradiction since we have infinite white issues (given)
Assume that there is no black point which is at a dist of one unit from a white ptPick a black pt and make a circle of radius 1 around itFrom our assumption, it's trivial to say that all the points on the circle will also be blackkEvery point inside the circle will have one point on the circumference which Is at a distance of one unit from it. So all the points inside have to be black as wellSo essentially you have a black circular patch. You can pick another point on this circle as the centre and repeat the same process. You'll end up with a plane filled with all black points and 0 white points, which Is a contradiction since we have infinite white issues (given)So the assumption is not possible. Theree has to be one white pt at a dist of 1 unit from a black pt
Case 2
All(infinite) the black points lie to the left of x=0
All(infinite) the black points lie to the left of x=0All(infinite) the white points lie to the right of x=2
All(infinite) the black points lie to the left of x=0All(infinite) the white points lie to the right of x=2The plane isn't filled with black and white pts, but you have infinite black and white points with no black point at a dist of one unit from a white pt
Answer:
You don't, because it's false. If all black dots happen to be on the line and white dots on the line (and the rest of the plane is neither white nor black), there is no such pair.
Explanation: