A hemireal number z can be written
z = r + mμ + nνwhere r, m, and n are real, and the special numbers μ, ν satisfy
μ*μ = ν*ν = 0, μ*ν = ν*μ = 1.Addition, subtraction, and any operation involving real numbers are
defined "the obvious way," and the conjugate of z is just z.
Multiplication of general hemireals is commutative but not
associative. Hemireals with ν=0 are the same as dual numbers.
The motivation for inventing/rediscovering (?) the hemireals was to solve, using finite numbers, what would otherwise be singular equations.