I think what he is trying to say is that as the steps reach the infinitely small, they appear to be very much like a straight line. Unfortunately, they never quite make it to being a straight line so you still travel the full 15.

Well in this case it doesn't matter much that you travel the 15cm in two different directions, it could as well be 15cm straight. The thing is, that no matter in how many small units you divide 15cm, the whole lenght together always stays 15cm.

Originally posted by TimTheEnchanter I think what he is trying to say is that as the steps reach the infinitely small, they appear to be very much like a straight line. Unfortunately, they never quite make it to being a straight line so you still travel the full 15.

Well in a Maths test it would make non calculator questions easier because you could just add the two side lengths together and say you thought that it wasn't a straight line...

Well in a Maths test it would make non calculator questions easier because you could just add the two side lengths together and say you thought that it wasn't a straight line...

I would never reach your position, scorch.
Because I would half to travel half the distance before the full distance, than half of the half, half of the remaining quarter, half of the remaining eighth, half of the remainings sixteenth.......half of the remaining 1/infinite

Or, I could never shoot an arrow from point A to B simply because the arrow will have to pass an infinite number of dots.

Returning to the original question, polymath is right: it doesn't matter how small you make the steps, you never have a diagonal line, you always have a stepped line.

You might think it was diagonal, but if you looked at the line through a magnifying glass, or a microscope, or whatever you needed to see the detail, you'd find it was still stepped.

Similarly if you took a line which was obviously stepped to you on the page and walked far enough away from it, it would look diagonal. But you would know the line itself had not changed. It would still be stepped. It would just look different because you weren't at the right distance to see its real form.

This is an age old paradox, the sort that used to abound in Scientific American in the 60s.

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