Your are confusing non-standard and dual numbers. The dual numbers are not ordered and contain non-invertible nilpotent elements such as h which squares to 0.
These things are different and I did mean dual numbers. The dual numbers do form an ordered ring. When you complain about certain elements being non-invertible, I think you are probably complaining that they aren't a field.
If a < b then a^2 < b^2. This is not true if you let a = 0 and b = h. The dual numbers do not have an ordering. You should provide sources and proofs next time because it seems like you are just making things up.
MikeBattaglia|1 year ago
clooper|1 year ago