- #1

stedwards

- 416

- 46

"First Order" infinitesimals are finite variables prepended with the letter ##d##.

Infinitesimal of any order, are prepended with ##d^n## where ##n## is the infinitesimal "order".

Finite numbers may be notated as ##d^0 B##. ##B## is any finite number.

Each transfinite number of would be the reciprocal of a infinitesimal. ##d^{-n}B = \frac{1}{d^{n}B}= \partial_{(n)}B##.

Examples: ##d^nC = d^mD d E^{m-n}##. ##n## and ##m## range over the integers, and ##d^n(d^m C) = d^{n+m}C##.

##d^mX<d^nY## for all ##X## and ##Y## where ##n<m## and ##X## and ##Y## are positive.

Is this a consistent system, or could there be cases where ##d^nX>d^mY## is true and ##d^nU>d^mV## is false?