Math question

[Ninteens 10+ year member]

Suppose that a man wants to cross to the far wall of a room that is 20-ft across. First, he crosses half of the distance to reach the 10-ft mark. Next he crosses halfway across the remaining 10-ft to arrive at the 5-ft mark. Dividing the distance in half again, he crosses to the 2.5-ft mark, and continues to cross the room in this way, dividing each distance in half and crossing to that point. Because each of the increasingly smaller distances can be divided in half, he must reach an infinite number of "midpoints" in a finite amount of time, and will never reach the wall.

Explain the error in Zeno's Paradox.

This has me stumped!//content.invisioncic.com/y282845/emoticons/verymad.gif.3f39c5c2fd57527b671fad3efdfac756.gif//content.invisioncic.com/y282845/emoticons/graduate.gif.d982460be9f153bb54e5d4cb744f6ae8.gif

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[Ninteens 10+ year member]

What! No one likes logic problems? LOL

 

[Flipx99 5,000+ posts]

Don't see the issue. A standard asymtope issue.

 

[Ninteens 10+ year member]

That is copied directly from the book. I can't see anything wrong, yet I'm supposed to

find and explain the error.

 

[Bloodstalker999 10+ year member]

NVM miss read the question

 

[Flipx99 5,000+ posts]

The dichotomy paradox

"You cannot even start."

“ That which is in locomotion must arrive at the half-way stage before it arrives at the goal. ”

—Aristotle, Physics VI:9, 239b10

Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on.

The resulting sequence can be represented as:

This description requires one to complete an infinite number of tasks in, what would surely need to be, finite time, which Zeno maintains is an impossibility.

This sequence also presents a second problem in that it contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion.

This argument is called the Dichotomy because it involves repeatedly splitting a distance into two parts. It contains some of the same elements as the Achilles and the Tortoise paradox, but with a more apparent conclusion of motionlessness. It is also known as the Race Course paradox. Some, like Aristotle, regard the Dichotomy as really just another version of Achilles and the Tortoise. However, they emphasise different points. In the Achilles and the Tortoise the focus is that movement by multiple objects is just an illusion whereas in the Dichotomy the focus is that movement is actually impossible.

 

[Flipx99 5,000+ posts]

me = slow

 

[Ninteens 10+ year member]

That still doesn't make full since. But, I'm writing the Dichotomy argument down.

That will be good enough for a freshman Problem solving class!

 

[Ninteens 10+ year member]

Blah, thinking = getting stoned!

 

[bryce-man 10+ year member]

haha i have this same paradox in my philosiphy class lol

but yeha he coudlt even get started casue for him to move to the 10 foot mark he has to move tho the 5 foot mark moving th midpoints closere and closer to the starting line

but in mathits bascily an asymtote(sp.. w/e) or a limit. i forgot

but yeah its confusing either way

good luck

 

[Tiger Bass 5,000+ posts]

I think I see the problem in the paradox but I'm not 100% sure. I'll have to check first.