Let \((X,\le)\) be a partial ordered set. If for every \(x,y\in X\) we have \(x\le y\) or \(y\le x\) we call \(X\) totally ordered and \(\le \) total order.
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- \(\mathbb{N}\), \(\mathbb{Z}\), \(\mathbb{R}\) are totally ordered.
Let \((X,\le)\) be a partial ordered set. If for every \(x,y\in X\) we have \(x\le y\) or \(y\le x\) we call \(X\) totally ordered and \(\le \) total order.