Order structure of real numbers
Set
| definiendum | $\langle \mathbb R,\le \rangle$ |
We define the total order over the real numbers (in the Dedekind cut model) via $r<s \equiv r\subset s$, i.e.
| postulate | $s \subseteq r \Leftrightarrow s\ge r$ |
Theorems
Inequality of arithmetic and geometric means (AM-GM inequality):
| $\frac{1}{n}\sum_{k=1}^n x_k \ge \left(\prod_{k=1}^n x_k\right)^\frac{1}{n}$ |
|---|
Reference
Wikipedia: Real number, Construction of the real numbers, Dedekind cut, Inequality of arithmetic and geometric means
Context
Element of
