Well, infinite divisibility can make strange things occur that can't happen in the "real world". An atom, for example, can be moved, but being sliced into small pieces and moved about how we like isn't a feature I know of.
You can get other rather unintuitive ideas from fractals, for example the Cantor middle-thirds set. http://www.math.buffalo.edu/~sww/cl...T/COMPACT2.html
If you ignore the compactness stuff for a moment, essentially you have a subset of [0,1] that has measure 0 but there exists a bijection from it to [0,1] i.e. it has length 1! That seems highly unintuitive, and in fact it should be impossible to construct such a set in the "real world" because matter is not infinitely divisible... at least not smoothly.
Matt Fahrenbacher
You can get other rather unintuitive ideas from fractals, for example the Cantor middle-thirds set. http://www.math.buffalo.edu/~sww/cl...T/COMPACT2.html
If you ignore the compactness stuff for a moment, essentially you have a subset of [0,1] that has measure 0 but there exists a bijection from it to [0,1] i.e. it has length 1! That seems highly unintuitive, and in fact it should be impossible to construct such a set in the "real world" because matter is not infinitely divisible... at least not smoothly.
Matt Fahrenbacher