no, he's jumping half the distance from himself to the wall each time. so the first time he was 4 inches form the wall, and he jumped 2 inches. now he's 2 inches from the wall and jumped 1 inch. no he's 1 inch from teh wall and jumped half an inch, so on and so forth. he will keep getting half as close to the wall as he is but never actually touching it
actually...
he will kind of touch the wall because of the way we define it.
right now if you are sitting in a chair you are really not in direct contact with it you are actually hovering over it because of that the atoms do this kind of wibly wobly magnet **** and they wont ******* touch eachother. so yeah eventually the frog will feel his nose against the wall.
Except I'd be willing to bet that there is a minimum distance for the movement to be called a "jump" not to mention the frog actually has to be able to jump such a small distance..so in reality the frog would eventually reach the wall. Mathematically he's ****** , but in reality he'll get there eventually.
I think what Stargate is trying to say is that because asymptotes really only work if the point is infinitely small like in a graph. A frog has a length of like, a couple of inches so if it reaches around 2 inches of distance from the wall it touches it!
The shark explained it terribly, let me help, I'm an octopus.
For the frog to reach the wall from where he is, he must first travel half that distance, but to travel that remaining half way, he must travel half of that, so he's now 3/4 of the way there. Then half of that, making him 7/8, then half of that, so he's 15/16 of the way there, and so on, meaning he can never reach the wall.
He gets closer and closer and closer, but each time must still half the distance before moving on.
And since we can't divide down to zero, just smaller and smaller (but positive) values, he can never actually reach the wall.
<< The way this tends to 0 but never actually touches it, can be represented thusly on a graph.
That line is called an asymptote and will go on forever (in both directions and in this case with a mirror image, but that's just because I was too lazy to get a better diagram), getting closer and closer to zero but never touching it.
infinte division by 2 say its 2 feet away and it goes half way so thats 1 foot then half of one foot is 6in then 3in then 1.5 in and so on. its a limit approacing infinity or an asymptote. its a thing you learn in precalc
well the term asymptote is what you learn. and yeah its obvious to some people but this guy didnt get the joke so i tried to explain the things in the joke.
between frog and wall is a set distance. the frog hops half that distance. a new distance has been created, which he hops half way through. in theory, he will never touch the wall, since he will allways be half the distance from frog to wall.
google Zeno's problem, and then google a picture of an asymptote, it'll kinda give you the best gist of what's going on without you having to be all "tl;dr, goddamn ************ science all up in dis bitch!" *ahem* I paraphrase, of course. Enjoy!
just think about it. imagine standing 5 units away from a wall, then walking halfway to the wall. now you're 2.5 units away. walk half the new distance, and now you're 1.25 units away. you could keep doing this and never reach the wall, since a/2 can't equal 0 unless a = 0.
Physics says that once you reach the Plank length however, that you've reached the wall in reality.
Technically, 9.9999 repeating does not equal one, but nobody cares enough to argue. The frog would never touch the wall by hopping half the distance, but, eventually, it will be impossible to hop half the distance.
Except anon was saying that 99.99999999999(repeating)% of 1 is equal to 1, when actuality it is not.
Sidenote: In my earlier comment, I said 9.99999 when I meant 0.999999. Oops