House Numbering Conventions

Postal adress consists of street name, house number and town name. The standard way of numbering houses is as follows:

natural numbers
The houses on the right side of a street are assigned even numbers and the houses on the left side are assigned the odd numbers. They go ascendingly from one fixed point on the street. We start indexing by 0.

negative numbers
When the street extends on the other side, the houses are assigned negative numbers.

real numbers
When a house is built between two existing houses with numbers a and b, the house in between is assigned a number in the interval (a, min(floor(a)+1, b)).

complex numbers
When the street has two axes and there is no straightforward way to flatten it, the imaginary axis is used for the second axis.

quaternions
When there are more orientations of doors in the street, the quaternion representing the orientation is added to the number. There are two quaternions representing a single orientation, so the higher one in lexicographical ordering is used. Therefore, the real part of the quaternion is always non-negative. The upward vector corresponds to the i axis, the direction of the street corresponds to the j axis and the vector pointing into the expected postion of the house correcponds to the k axis.