Space? if you moved only 1/2 distance to an object everytime you moved, would you eventually reach that object

Question

for example: if you took the head of a pen and moved it exactly half distance to a piece of paper everytime you moved the pen, would that pen head eventually hit that paper?

Answer 1

For all intentive purposes yes, what you're doing is taking the limit of (1/2)^x as x approaches infinity. In other words, you keep cutting the distance by 1/2 every time so you get 1/2, 1/4, 1/8, 1/16 and so forth. After you do this just 1000 times you're less than 7.8 * 10^(-31) units away (where units are cm, inches, feet, whatever you're using). That is insanely small. Doing that 1000 times, puts you so close to zero my calculator concedes to being accurate. So no, you never reach ZERO but no one would be able to tell the difference, not even atoms.

Answer 2

If the moving object is a point (a dot with 0 diameter), it will never reach the destination. In real world the moving object has some size and when the distance between the destination and the position of the moving object is less than the size (say length) of the moving object, then the object will have reached the destination. The case of the pen is that the distance between the head and the paper is less than the diameter of the head and hence the head should touch the paper. That is how all things in real world reach a destination.

Answer 3

No, you will never reach the object because even though you can get physically close you're only moving half of the distance that's left and it will keep getting infinitesimally smaller and you'll keep multiplying the number by 1/2 which will never get you to the object.

Answer 4

This is called Zeno's paradox, it is ancient. He says that there is no motion, because before a thing can go the whole distance to another location, it has to go half the distance first, and it has to go half the half-distance before it can go the half-distance and so on until you get down to very tiny distances. Modern solutions involve a minimum distance, beyond which there is no further division, so a thing can do the deed.

Answer 5

yes if it was a foot away it would take 16 moves however it would only hit due to the bulkyness of the pen head if it was a more minute item it would much longer to achieve this. The ultimate answer is yes it would reach because its a constant move foward, but it would take forever to reach the destination of the desired target!!!!

Answer 6

No... Mathematically, if you continuously divide by 2 (or cut in half), you will never reach 0 (or the end point). You will however, become VERY close with only a TINY decimal point separating the two objects.

Answer 7

no, if you always move half the distance, lets say 10 inches. first you would move 5 inches, then 2 1/2 inches, then 1 1/4 inches.... you would never get to it, because you would always cut the remaining distance in half..... so once you got down to .00005 then you would move.000025 so you would never get there

Answer 8

Infinite number of moves required. Impossible to achieve contact

Answer 9

Uh-oh! I in basic terms remembered Prue and Paige Halliwell from Charmed! Having their capability could be great. i could use it for inner maximum income yet I won't abuse it. nicely,...perchance i'm going to revenge on some those that aggravated me in the previous *evil grin* yet this is all!

Answer 10

no..you would never get to it it is impossible in any way...you would get so close but you cant reach it...try dividing 100 by half each time ..see what you get...tell me when u get to 0....o wait im not going to live for an infinite amount of years nvm..sorry for sounding mean...im just realy tireed and had a long *** week