MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
show/hide this revision's text 3 added 23 characters in body

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 an integer-valued a dimension with an integral number of coordinates. However, does statement one hold in a fractional dimension?
show/hide this revision's text 2 Updated volume growth rate.

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 3/42^3/4

To me, it is obvious that both of these hold in an integer-valued dimension. However, does statement one hold in a fractional dimension?
show/hide this revision's text 1

Is the notion of fractional dimension compatible with considering a dimension a set of n-tuples?

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 3/4

To me, it is obvious that both of these hold in an integer-valued dimension. However, does statement one hold in a fractional dimension?