The velocities and of two bodies moving along a line obey, by the special theory of relativity, the addition rule
where is the velocity of light. As is unreachable for any material body, it plays for the velocities of the bodies the role of the infinity. These velocities thus satisfy always
By (1) we get
for ; so behaves like the infinity.
One can define the mapping by setting
which is easily seen to be a bijection.
Then the system may be checked to be a ring and the bijective mapping (2) to be homomorphic:
Consequently, the system , as the isomorphic image of the field , also itself is a field.
Baker  calls the numbers of the set , i.e. ,
the Einstein numbers.
- 1 G. A. Baker, Jr.: “Einstein numbers”. –Amer. Math. Monthly 61 (1954), 39–41.
- 2 H. T. Davis: College algebra. Prentice-Hall, N.Y. (1940), 351.
- 3 T. Gregor & J. Haluška: Two-dimensional Einstein numbers and associativity. arXiv (2013)