Question

1. There are infinite black and white dots on a plane. Prove that the distance between one black dot and one white dot is one?

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Answer 1

Is this not a thought experiment asking you to reason that if there are an infinite number of dots then somewhere there must exist a black dot of unit length away from a white dot. Or it could be purposefully being vague on what it means to be unit length and you could argue that one unit is the distance between two points you picked.

Answer 2

think about it in this way we are tossing dice, then the probability of getting an head and tail is not always 50-50

if we do it practically, but it will be almost 50-50 if we will keep on increasing the numbers of expirement

like wise in this case, it's given infinite.

so we can use the concept that if we will keep on increasing number to infinite

chances will be fair

it's only a thought experiment

theoretical approach of looking at it

so, we can say that the probability that the difference between one black dots and white dot is 1 is 100%