# Interesting calculus problem

1. Dec 13, 2003

### wunderkind

Prove to me mathematically that if I start walking from one end of a room that I will eventually reach the other side. Be sure to include all your formulas!(hint:remember theorems!)

2. Dec 13, 2003

### master_coda

The conditions you've provided aren't strong enough. If the speed you're walking at decreases over time fast enough, then it's possible that not even an infinite amount of time would be long enough for you to reach the other side.

3. Dec 13, 2003

### BigRedDot

On the other hand, it may be that space is discrete, and that a continuous approximation does eventually break down and stop being useful. (And alas, pragmatic sanction really is the only justification we are left with for our mathematical creations.) There may exist a minimum length scale, below which it is not possible to take steps. In which event, assuming you walk along a "straight line path" from one end of the room to the other, there are only a finite number of steps needed. Then, you will always reach the other side of the room as long as there is not an "infinite" amount of time between any two steps.

4. Dec 17, 2003

### hemmul

prooving wrong

There is nothing to proove. This problem, at least how it is stated at present, has no true proof.

The problem statement lacks at least the following:

1) Direction in which you are walking.
if you walk along the wall you will never reach the opposite wall.
2) Velocity
velocity that equals zero is also velocity, isn't it? :)
3) the law of changing of the velocity in time.
4) velocity of the opposite wall :)
Consider a train on a railway station! You start walking from the back end to the cockpit ("opposite wall")... in the way, a policeman asks you to leave the train because you have no ticket. The result - you are on the station, train is half a way to [sensored] city... on the way to that city, because of the malfunction in engines the train explodes... there is no train any more... no cockpit... no "opposite wall"... you will never reach it...

:)

i just wonder, what theorems were we supposed to use, to proove your problem as is?

Last edited by a moderator: Dec 17, 2003
5. Jul 23, 2004

### mathwonk

in fact i have never made it to the end of my back yard but have started in that direction many times.