If I throw a ball at the wall, when it has travelled halfway, it still has half the distance to travel. As it continues, the fraction left to travel continues i.e. one quarter to go, one eighth to go, one sixteenth to go, etc. since the denominator of the distance continues to double... I am thinking mathematicaly speaking, the ball never reaches the wall.
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2Zeno? Is that you? – Steven Stadnicki Jul 05 '15 at 04:51
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Nope. The turtle beckons... – Panglossian Oporopolist Jul 05 '15 at 04:58
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5Have you actually tried throwing a ball at the wall? What happened? Please see [ask] for future reference, and try to include more context in Questions if you wish Readers to respond appropriately. – hardmath Jul 05 '15 at 05:01
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When an object moves along a line from point A to another point B in t seconds, it passes through infinitely many points on that line. The arrival at each point can be seen as an event. As counter-intuitive as it may seem, infinitely many events would occur in that t seconds in moving from A to B. The ancient Greek philosophers didn't understand this idea. We take it for granted. – Dan Christensen Jul 07 '15 at 20:14
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Mathematically speaking: $$\sum_{n=1}^\infty\frac{1}{2^n}=1$$ You're just restating Zeno's, *ahem*, "paradox" (Wikipedia link).
Zev Chonoles
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The ball reaches the wall since the time interval required to go half of the remaining distance to the wall decreases by a factor of $2$ with each successive step (assuming constant speed throughout the journey).
So, for the first step, the ball travels $1/2$ the distance to the wall and takes a time, say $t_1$.
For the second step, the ball travels $1/2$ the remaining distance to the wall ($1/4$ of the original distance), taking $\frac12 t_1$ to get there.
Continuing, we have the total time that it takes to reach the wall is
$$\sum_{n=0}^{\infty}\frac{t_1}{2^n}=2t_1$$
which is certainly less than "forver."
Mark Viola
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