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My thought might be a bit weird or maybe childish, but I can not find anything to object it or to prove that it is wrong.

As a basic definition of a straight line that it is an infinite number of points that are connected together.

Regardless the length of that straight line, it consists of infinite number of points.

I've thought about breaking that line into two halves, so I would get one half of infinity(starting from zero and going to +ve infinity and omitting the other half from -ve infinity to zero), what if I keep breaking the line for infinite times? the conclusion would be that the straight line is nothing but a point?

If it was an infinite number of points, I would always get infinity even if I break it to an infinite number of times, right?

I am really confused and would like someone to help me how to think it out.