Re:Mathematician Wins $3M Prize for 'Magic Wand Theorem'
by thaumasiotes on Sunday September 08, 2019 @04:50PM
(#20913330)
> then you come arbitrarily close to any other point in the room
It looks like the claim is that all but a finite number of points are actually achieved. This is a stronger result -- you can easily prove from that claim that you can get arbitrarily close to any point (because a neighborhood of any radius contains an infinite number of points, and therefore contains a point that is achieved), but you can't go the other way. It's quite possible to be arbitrarily close to every point while failing to hit an infinite number of points.
It looks like the claim is that all but a finite number of points are actually achieved. This is a stronger result -- you can easily prove from that claim that you can get arbitrarily close to any point (because a neighborhood of any radius contains an infinite number of points, and therefore contains a point that is achieved), but you can't go the other way. It's quite possible to be arbitrarily close to every point while failing to hit an infinite number of points.