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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
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
Context
Element of
