Assuming i walk in a straight line, if i was to walk half the distance to the shop and then stop, then walk half the distance i 've just covered and stop, then walk half the distance again etc, will i ever reach the shops or will my journey continue ad infinitum?
2007-03-04 01:54:24 · 10 answers · asked by famouslighteater 2 in Science & Mathematics ➔ Mathematics
In theory you will never reach the shops, but in fact you will soon reach a half distance that would be infinitesimally too small for you to move, thus you would stop moving, or over-shoot your desired amount of movement, and reach the shops.
2007-03-04 02:01:27 · answer #1 · answered by DAVID C 6 · 4⤊ 0⤋
In theory, no - you will never reach the shops. However, after many 'halvings' of the distance between yourself and the first shop, you will soon be close enough to reach out, open the door & shout your order to the proprietor. You might never get in, but at least you can still do the shopping.
Good luck!
2007-03-05 05:54:15 · answer #2 · answered by general_ego 3 · 0⤊ 0⤋
This is an example of Zeno's paradox. Of course, in terms of the paradox you will never get to the shops. The paradox assumes that you can keep on dividing time into smaller and smaller amounts. This takes us into the realms of quantum theory which tells us that units cannot be infinitely small - there is a smallest unit of time. The theory shows that it is impossible to have an interval of time smaller than 10^-43 seconds. That is a decimal point followed by 42 zeroes and then a 1. This is known as the Planck time.
2007-03-04 03:00:49 · answer #3 · answered by RATTY 7 · 1⤊ 1⤋
You will never reach the shop as the faction covered will never reach one, just a number very close to one, ie.
(1/2) + (1/4) + (1/8) + (1/16) + (1/32) + (1/64)...
2007-03-04 02:12:08 · answer #4 · answered by Kemmy 6 · 1⤊ 0⤋
This one is as old as the hills. Well, the Ancient Greeks anyway.Nope, you wont get to the shops mathematically,but in the real world you'd split the atom on the way, and it's neutrons,etc.,so you'll need very powerful footsteps!
2007-03-04 05:17:45 · answer #5 · answered by jonal 7 · 1⤊ 0⤋
No, you will be stuck like a fool outside Tescos, and people will laugh at you!
You're better off just walking the whole distance at once. Especially as its raining out...
2007-03-04 08:00:49 · answer #6 · answered by nick 4 · 0⤊ 1⤋
Zenos paradox - you'll never reach the shops, mate!
2007-03-05 03:47:57 · answer #7 · answered by Anonymous · 0⤊ 0⤋
David C's answer is good. Just thought I would add, this problem is called Zeno's Arrow Paradox... http://en.wikipedia.org/wiki/Zeno's_paradoxes#The_arrow_paradox
2007-03-04 02:05:42 · answer #8 · answered by paralegaltechnik 3 · 1⤊ 0⤋
you will reach them when they are already closed. They close at 5 today, you know. Plus, you are annoying people who is actually trying to get somewhere and are walking behind you..
2007-03-04 02:01:57 · answer #9 · answered by Sheldon 6 · 0⤊ 1⤋
you will never reach the shops
2007-03-04 08:10:05 · answer #10 · answered by Anonymous · 1⤊ 0⤋