Dimensions and Directions.

[math]\mathbb{R}^{0} = \{p\}[/math], i.e. the set containing one element.

 

Really, by the distance between two (near by) points you are assigning a length to the vector that joins them. This requires a metric as we have discussed.

Hello,

I have realised that the idea I have has not been thought of before, which doesn't matter, all that matters is if it adds up.

I start by saying establishing an origin requires two factors of comparison simply because the singular has no relative definition. In simple terms we create 'empty space' and a 'dot' to define the dot as a singularity.

0d is actually created using an 'is/isn't' comparison. We say the origin 'is' as opposed to 'isn't', and a singularity is really comparitive opposites.

We can go into complex feilds but the fact is, no concept of origin can be definitive wthout an 'isnt' for comparison, simply because singularity has no real relative definition.