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If you look back at the picture with the green and blue line. Imagine n goes to infinity are there still vertical lines left?

Of course there are, they are just infinitesimally small. Their sum doesn't change, it's still two.

My previous question was poorly phrased.

The blue line converges to the green line. But the green line has no length in the vertical direction. So where did all the vertical lines go?

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