Math Question?

Question

If a frog is one foot away from a wall and jumps halfway to the wall (It is now 6 inches away). If it keeps jumping halfway to the wall will it ever reach the wall?

Answer 1

This site uses calculus to show that the frog will.
http://www.fortunecity.com/lavender/eraserhead/708/math.htm

"The first is the famous "frog and the wall" problem. Iplace a frog one foot from a wall and tell him to jump half way tothe wall, then jump half way to the wall again, then jump half wayto the wall again, and keep going. Does the frog ever reach thewall? Of course he does."

You can find the complete explanation in the section for problem 11.

Answer 2

Your question can be translated to can we divide a number by 2 a finite number of times and reach 0.

The answer is no.

However,

Lets assume that there is a finite length of of space that is atomic (Plank's constant.) Eventually you will reach a point where you have jumped to the atomic unit of space just before the end. Since this is an atomic unit of space, you cannot divide it further. If you choose to jump, you either go all the way or you don't move at all. If your definition of jump is to round up, you will indeed reach the destination. If your definition of jump is to round down or truncate, you will never reach the destination.

Answer 3

This is a rewording of Zeno's paradox.
http://en.wikipedia.org/wiki/Zeno's_paradox#Achilles_and_the_tortoise

The short answer is no. Of course we're going on the assumptiont hat the frog can always jump half of the remaining distance. At some point, probably less than 100 jumps in fact, we'd be asking the frog to go a distance that's smaller than an atom's nucleus.

Answer 4

No, I don't believe so. You're asking if the frog always jumps half the distance he jumped before, will he eventually reach the wall?

The distance is 1. the frog jumps half of that, so he's travelled 0.5. If he jumps half of 0.5, he'll jump 0.25 and be at 0.75.

And so on:

0.75 + (0.25 / 2) = 0.75 + 0.125 = 0.875
0.875 + (0.125 / 2) = 0.875 + 0.0625 = 0. 9375
0.9375 + (0.0625 / 2) = 0.9375 + 0.03125 = 0.96875
0.96875 + (0.03125 / 2) = 0.96875 + 0.015625 = 0.984375
0.984375 + (0.015625/2) = 0.984375 + 0.0078125 = 0.9921875
0.9921875 + (0.0078125/2) = 0.9921875 + 0.00390625 = 0.99609375
0.99609375 + (0.00390625/2) = 0.99609375 + 0.001953125 = 0.998046875

You'll find you can come really close to 1, but you won't ever reach one. To reach one, you'd need another 0.5, and you won't ever get it if you keep adding half.

Answer 5

No. Using that scenario, the frog will never reach the wall.
It will, however, get _extremely_ close to the wall.

Answer 6

no, if it keeps jumping halfway to the wall it wont jump all the way to the wall.

Answer 7

Yes
It will take 34 jumps

the 33rd jump will be 0.000000001
34th jump reads 6.98491931-10

not unless I am reading it wrong.

Answer 8

This is the Zenon paradox.
It would never reach the wall

Answer 9

According to the Paradox of Zeno the answer is NO.

Answer 10

Technically, no, because you can always take half of the distance. (Eventually, he'd be jumping infinitely small amounts.)