Skip to main content
MathOverflow

Return to Question

added 23 characters in body
Source Link
gonzo_floyd
gonzo_floyd
  • 13
  • 4

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-valueda dimension with an integral number of coordinates. However, does statement one hold in a fractional dimension?

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 dimension. However, does statement one hold in a fractional dimension?

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?

Updated volume growth rate.
Source Link
gonzo_floyd
gonzo_floyd
  • 13
  • 4

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 32^3/4

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

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?

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 dimension. However, does statement one hold in a fractional dimension?

Source Link
gonzo_floyd
gonzo_floyd
  • 13
  • 4

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?