Walking Towards A Wall

Calculus Level 1

Suppose you are standing one meter from a wall, and you begin walking towards the wall. With each step, you cover half the distance between you and the wall. If you do this at a rate of one meter per second, will you ever reach the wall?

Yes No Cannot be determined

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Justin Malme by Justin Malme , 36, USA

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1 solution

Justin Malme
Jun 9, 2016

Relevant wiki: Zeno's Paradox

You will reach the wall in one second, having taken an infinite number of steps. Since each step covers half the distance between you and the wall, it's easy to assume that you will get infinitely close to the wall, but never reach it. However, since you are traveling at one meter per second, you will reach the wall in one second, though you will take an infinite number of steps in that one second as well. The thing to remember is that with the declaration of a rate of speed, time becomes a factor. So at half a second you have traveled half a meter, at three quarters of a second you have traveled three quarters of a meter, and at 0.999... seconds you have traveled 0.999... meters. However time will eventually hit 1 second, and thus you will travel one meter. This is similar to Xeno's Dichotomy paradox.

27 Helpful 5 Interesting 5 Brilliant 6 Confused

Can't we just use that there's a series of distances obtained(dist. b/w the man and the wall) after taking infinite steps to reach the wall.So a convergent series is obtained.

Babu Bisleri - 3 years, 1 month ago

it is a bit ridiculous! i understand that this thing (1/2+1/4+1/8+...) converges to 1... but here's an issue: the CLOSER you come to the wall the MORE steps PER SECOND you must make (to maintain the constant speed of 1m/s... and right before the wall you must make INFINITELY MANY steps per second! so it's a bit absurd! i understand, that it's a MATH PUZZLE and it kind of doesn't have anything to do with PHYSICS and reality.. but still!...:))) The question in the puzzle is put in a physical manner: "will you ever reach the wall"... meaning it should take finite time to do it! So if "you" (like any other physical object) can't make infinitely many steps per second, "you" won't be able to reach the wall in finite amount of time... :)

Nik Gibson - 2 years, 10 months ago

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That's exactly what I was thinking. Mathematically valid, but not physically valid. It should not have been presented in a physical context.

Christopher Ali - 7 months ago

Good point :)

Mashael Fakhro - 1 year, 3 months ago

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