If you dig a hole in the ground, then fill it halfway, then fill it with half of the remainder, then again with only half of the new remainder and so forth, will you ever fill the hole?

Emon the body's buried enough we need to get out of here before someone sees

****. People will answer this correctly after the first week or so of calculus.

I predict that this thread will degenerate to the .999=1 debate.

Clearly I didn't pay attention in calculus.

That's a infinite geometric series that converges at 1 as the number of iterations reaches infinity.

So, no.

Yes. Matter cannot be divided infinitely.

An infinite number of mathematicians walk into a bar. The first orders 1 beer. The second order 1/2 of a beer. The third orders 1/4th of a beer. The bartender says, **** this, and pours two beers.

Are you looking for an abstract mathematical answer (no) or are you looking for the real answer (yes)?

of couse it will, cause as people said, matter cannot be divided infinately, so eventualy you will reach the stage where you only have molecules.

Clearly the only way you can objectively define a hole as filled is by satisfying a statistical definition of 'filled' for a hole of the given size. This statistical definition can be determined by asking a sample group if a hole is 'filled' for each iteration. A control group will just be asked repeatedly if an empty hole has been filled.

not to mention that the fill will be less compressed when it is put back into the hole than it was when it was dug out.

First of all, let's assume that we're not talking about a real-world situation (duh), so let's ignore physics. Obviously eventually we'd get to a scale where you'd have quantum effects.

So let's take it as a though exercise in math. One thing you don't quite specify is the timing of your operations, but the way you phrase it, I'll assume that you mean that each discrete step (filling the hole again by half) is done at a regular interval. In this case, the answer is: "You will never fill the hole in a finite amount of time."

What makes this a slightly different question from the usual Xeno's paradox is the introduction of discrete steps that are performed at a constant interval. Xeno phrases his paradox this way, too, but he calls up the image of motion at constant velocity... from which any calculus student would tell him that, as he shrinks the distances traveled, he also shrinks the times, so that series does converge within a finite timespan.

Who said anything about a finite amount of time?

I did. If someone answers the question "will you ever...?" with "yes", the followup question is normally "When?" In answering that question, there's no difference between "never" and "in an infinite amount of time from now".

whats with all these lately

Then answer is no (ignoring that matter has a limit to division), because you keep adding a fraction of the currently unfilled space, yet never filling the space it self. So no, you'd never fill the hole.

I was going to post something like this

but

dumber

or you could dump all the dirt back in at once and be done with it

Or, after half a minute, you put half the dirt back in, then after a quarter of a minute, you put in half the dirt that's left, then after an eighth of a minute, you put in half the dirt that's left...

I think that's the most elegant way to do it.

what if you smoke a bowl and **** digging holes?

I giggled at that bit.

/quip about not being able to have half a hole

And I say yes because I'm going with a real world example where the ground isnt level or completely flat.

it'll get full enough too be considered near as damnit full! so i voted yes

This is also true. Since the hole approaches 'full' as time increases without bound, you can approximate fullness to any degree of satisfaction.