High School Representation of infinitesimals in different ways

[Mike_bb]

Hello.

There are 4 types of infinitesimals:

1) dx=1/N, N is the number of elemets of the set of the natural numbers (letter N is used to indicate the cardinality of the set of natural numbers)

2) Hyperreal numbers: ε=1/ω, ω is number greater than any real number.

3) Surreal numbers: { 0, 1, 2, 3, ... | } = ω , { 0 | 1, 1/2, 1/4, 1/8, ...} = ε, where ω is a transfinite number greater than all integers and ε is an infinitesimal greater than 0 but less than any positive real number.

4) Nilpotent infinitesimals are numbers ε where ε² = 0

Infinitesimals are represented in different ways. What is difference between them?

Thanks.

 

[PeroK]

Infinitesimals are represented in different ways. What is difference between them?

An infinitesimal difference, perhaps?

 

[Mike_bb]

An infinitesimal difference, perhaps?

Yes