Question

there are infinite black and white dots on a plane. prove that the distance between one black dot and one white dot is one unit


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Answer 1

Answer:

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Explanation:

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Answer 2

Explanation:

Taking 1unit= X

Now let's say that the number of whites and black are equal becuase they both are infite (means they have same values)

Now I know that it's not confirm that the distance between each point will be 1 unit but since the number of points are both infinite means

∞+∞=2∞

well this not works on infinity but it's a huge concept but in this situation let ∞=Y

so now we can say that y+y=2y

ok hope that is clear

Now let's calculate the area of plane the palne which is carrying points and must be rectangle or Square so

ar of plane =l×b

but the the length and breadth are equal to no. of points

so area = no.of points on l× no.of points on b

now total no of points are 2y and the no. of points of white and black are Same

so area = 2y

and length of each side = y

so according to unit constant ,

the distance between each point to manage the area in the same no. of points call only be 1 unit (this property only works in special conditions like here)

we have proved now that the distance between each point is a unit