In fact, R can be defined as the only ordered field with that quality. If ( F, +, ×) is a field and ≤ is a total order on F, then ( F, +, ×, ≤) is called an ordered field if and only if:īoth ( Q, +, ×, ≤) and ( R, +, ×, ≤) are ordered fields, but ≤ cannot be defined in order to make ( C, +, ×, ≤) an ordered field, because −1 is the square of i and would therefore be positive.īesides from being an ordered field, R also has the Least-upper-bound property.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |