Originally Posted by

**ShinAce**
Because infinite steps does not make any sense. If you can see that there are steps, there aren't an infinite number of them. If there's an infinite number of them, you can't see if they are steps or slopes. So what does infinite steps imply? If you imagine a bunch of little steps, you say 20 feet of material are required. I ignore that there are any steps at all and just make a ramp. You would need 20 feet because you want to build a staircase with n steps. I would need 14.14 feet because I'm not building steps, I'm making a ramp. I just lay one piece of wood down and call it a day. Don't take the analogy too seriously. I'm not saying that numerical integration gives an answer different than integral calculus. If you really are making little steps, then you need 20 feet of material. If you think infinite steps requires 20 feet, go ahead and buy 20 feet of wood. Your staircase will look and feel the same as my ramp, and I'll save some money on material.

, with infinitesimal steps you still need 20 feet of wood.

This time you're the one using intuition rather than formalism to argue your case.

__________________________________________________

Reductionist and proud of it.

Being ignorant is not so much a shame, as being unwilling to learn. Benjamin Franklin

Chase after the truth like all hell and you'll free yourself, even though you never touch its coat tails. Clarence Darrow

A person who won't read has no advantage over one who can't read. Mark Twain