# Tagged Questions

**11**

votes

**1**answer

585 views

### Converse to Banachâ€™s fixed point theorem for ordered fields?

Suppose $R$ is an ordered field. Call a continuous map $f: R \rightarrow R$ a contraction if there exists $r < 1$ (in $R$) such that $|f(x)-f(y)| \leq r |x-y|$ for all $x,y \in R$ (where $|x| := ...

**2**

votes

**4**answers

925 views

### What are examples of ordered fields that do not have the Archimedean Property?

Are the computable numbers one example?

**20**

votes

**2**answers

617 views

### How much choice is needed to show that formally real fields can be ordered?

Background: a field is formally real if -1 is not a sum of squares of elements in that field. An ordering on a field is a linear ordering which is (in exactly the sense that you would guess if you ...