Coming from someone who is "used to" this idea for a long time, I'm not sure how helpful my explanation would be to a learner, but I decided to take a shot at i

Coming from someone who is "used to" this idea for a long time, I'm not sure how helpful my explanation would be to a learner, but I decided to take a shot at it, just in case it helps someone. That said, in my experience, a significant part of "understanding" involves getting used to things and expanding the scope of what you consider "natural". -- Suppose you wish to walk from 0 to 1. You'll have to walk half the distance. Then half of the remaining half. Then half of the remaining quarter. Then half of the remaining eighth. If you keep doing this "asymptotically", you will get very very close to 1 and (almost) reach there. That's the basic idea. This is also known as Zeno's paradox: https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Paradoxes_of_motion https://en.wikipedia.org/wiki/Zeno%27s_paradoxes#Paradoxes_o... Instead of halving step sizes on each iteration, you could reduced by a different fraction. In general, this is called a geometric series: https://en.wikipedia.org/wiki/Geometric_series https://en.wikipedia.org/wiki/Geometric_series When the ratio is (2/3), after two steps you overshoot 1. (You can see that (2/3) = 0.66, (2/3)^2 = 0.44 )