Hi there,

I am trying to teach a friend about higher-dimensions and I have explained them in the following two manners:

1. A higher dimension, e.g. the 56th is the set of all 56-tuples.
2. A fractional dimension, e.g. 3/4 means that when size doubles, volume increases at a factor of 2^3/4

To me, it is obvious that both of these hold in a dimension with an integral number of coordinates. However, does statement one hold in a fractional dimension?