- #1
Mike_bb
- 57
- 3
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.
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.