I was reminded of this by the post below about lines of longitude.
There is an old riddle that says that if I walk a mile south, then a mile east (or west), then a mile north, I will be back where I started, perhaps having seen a bear on the way. So where am I?
The well-known answer is 'The North Pole'.
But the number of such points on the earth's surface is infinite (if we leave out the bear) of which the North Pole is only one. Explain.
(Those who already know the answer, please give time for others to work it out from scratch. Ta.)
Sorry, New Judge, to quote a better mathematician than myself "common sense is amid alien corn in the land of the infinite". Common sense says the same as you said - surely a finite line cannot contain an infinite number of points? - but Georg Cantor proved otherwise back in late Victorian times. It's no use arguing.
Ok I'll give you that one chakka. The idea of the east/west part of the journey resulting in returning to the same place as that leg of the journey started, wasn't an eventuailty I considered.
As I said in my first post I think Chakka is cheating. The whole point about the riddle is that it will work for ANY *(see below) distance from the North Pole, not just 1 mile and you always get back to the north pole.
* assuming you don't go so far south that you reach the south pole or start coming back up towards the north pole.
vascop - you can form a new riddle, if you like, by adding those extra requirements, but they are not part of the original. Perhaps you could give us your new version here.
New Judge - as others have explained, you can certainly have an infinite number of points on a line of finite length. This is because a point has no dimension.
Thanks, canary42 and Old Geezer for seeing things straight.
My version would be:
If you walk any distance south (as long as you don't reach the south pole, go over it and start coming north again), then go the SAME distance east or west, and then the same distance again north and find yourself back where you started, where must you be?
Thanks, vascop, for your rather long-winded riddle. Since it's not the one I posed, nor the original involving a bear, it isn't, of course, relevant to this thread. But I did ask for it so thank you.
Also you couldnt walk any distance south from the north pole because in all likelihood you would hit open water of the arctic ocean preventing you walking any further. (dependant on season and global warming)
We could change "walk" to "travel" but that is not in the original riddle.
//Also you couldnt walk any distance south from the north pole because in all likelihood you would hit open water of the arctic ocean preventing you walking any further.//
^ Canalman is correct. Infinity is an odd thing. For example a koch snowflake can have an infinite perimeter. I remember seeing a TV programme once which showed that the coastline of Britain is of infinite length when you take account of all teh nooks and crannies
surely if you walk a mile South, then a mile East, then a mile North you are still a mile East
of where you started? to rectify this you would need to walk an additional mile West.
I think it only works on a perfect sphere on a sphere any start point could be considered then to walk south is possible, to walk e or w then because of the curve of the spher you would return to the start if you walked back the same distance. reversing the North to south with a south to north. Because you have walked east or west in a straight line you are still one mile south of your start point
