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Suprema of directed sets

Let $(X, \le)$ be a partially ordered set. We call a subset $S \subseteq X$... ... a chain if each two elements in $S$ are comparable with respect to $\le$ (in other words, $S$ is linearly ordered wi …
Jochen Glueck's user avatar
31 votes
Accepted

Characterizing $\mathbf{R}$ as an ordered group

The linearly ordered group $(\mathbb{Z},+,\le)$ is a counterexample, but that is probably not what the OP had in mind. To give a detailed description of the situation, let us use the following notatio …
Jochen Glueck's user avatar