If we choose rational numbers to represent points on a line then there will be gaps on the line and consequently the plane will be full of holes. Then we cannot say that two non-parallel line must intersect on a point (because they may meet at the gaps). So obviously we need point arranged more densely than rational number. I was wondering do we necessarily need real number line for euclidean geometry or we can stop at earlier infinity. After writing this far I realize it points to continuum hypothesis. But I don't know enough and will highly appreciate your input and comment. I am not a student of mathematics but dabble with its concept every now and then.