What's the defintion of a real field?

## 1 Answer

The approach Rudin takes is this.

Describe the field axioms and the ordered field axioms. Claims that there exists an ordered field which satisfies the least upper bound property. This field is called the real numbers and is denoted as R (note this is well-defined because any ordered field satisfying the LUB property is isomorphic to R). Rudin does not construct R in chapter 1. He leaves that to an appendix by using Dedekind cuts. Note there is also an exercise in Chapter 3 which gives an alternative construction, and in fact, a generalizable construction; this one is known as the equivalence class of Cauchy sequence construction (full and glorious details may be found, for example, in Introductory Real Analysis by Kolmogorov)

## Related questions

0 like 0 dislike
1 answer
Are the S3/S4 Edexcel Further Maths units useful to become an actuary? Topics include sampling, unbiased and biased estimators, confidence intervals and significance test...
0 like 0 dislike
20 answers
Considering leaving the actuarial profession. What are some interesting fields you've heard of former actuaries going into? How did they get into the new field?
0 like 0 dislike
9 answers
Has anyone successfully guessed on like half of the questions on an exam and still passed?
0 like 0 dislike
2 answers
The Actuarial Education Company finally removed the dictionary definition of "final solution" from their binders
0 like 0 dislike
2 answers
I did this all wrong but got the right answer? Took half of .075, used d=(1+i)/i to get discount rate, and just added. Decimal was off, but i got the numbers right. Luck?...