A total ordered set \(X\) is called well ordered if each subset contains a smallest element.
Examples Link to heading
- \(\mathbb{N}\) is well ordered.
- \(\mathbb{R}\) and \(\mathbb{Z}\) are not well ordered, consider for example \((0,1)\) or \(\{\ldots ,-2,-1,0\}\).
Remarks
- According to the well-ordering theorem every set can be well ordered.