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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 8th 2021
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/archimedean+group/1">v1</a>, <a href="https://ncatlab.org/nlab/show/archimedean+group">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 16th 2021
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   Author: Todd_Trimble
   Format: MarkdownItexReplaced the wrong sentence that the real numbers form a terminal archimedean group. <a href="https://ncatlab.org/nlab/revision/diff/archimedean+group/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/archimedean+group/5">v5</a>, <a href="https://ncatlab.org/nlab/show/archimedean+group">current</a>

   Replaced the wrong sentence that the real numbers form a terminal archimedean group.

   diff, v5, current

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 16th 2021
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexReplaced the wrong sentence that the real numbers form a terminal archimedean group. <a href="https://ncatlab.org/nlab/revision/diff/archimedean+group/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/archimedean+group/5">v5</a>, <a href="https://ncatlab.org/nlab/show/archimedean+group">current</a>

   Replaced the wrong sentence that the real numbers form a terminal archimedean group.

   diff, v5, current

4. • CommentRowNumber4.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJun 16th 2021
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexThe claim appears to be repeated at [[real number]]: > Alternatively, an archimedean group is terminal if it is the terminal object in the category of archimedean groups.

   The claim appears to be repeated at real number:

   Alternatively, an archimedean group is terminal if it is the terminal object in the category of archimedean groups.

5. • CommentRowNumber5.
   • CommentAuthorDavidRoberts
   • CommentTimeJun 16th 2021
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexHmm, this doesn't make sense >The positive integers are embedded into the function group $A\to A$ unless I assume that $A\to A$ is automorphisms of $A$. That is, unless $A$ is abelian, somehow forced by the linearity of the ordering on $A$.

   Hmm, this doesn’t make sense

   The positive integers are embedded into the function group $A\to A$

   unless I assume that $A\to A$ is automorphisms of $A$. That is, unless $A$ is abelian, somehow forced by the linearity of the ordering on $A$.

6. • CommentRowNumber6.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 16th 2021
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexThe Wikipedia article on archimedean groups does say that they're abelian, but perhaps you're right perhaps in that this ought to be said first. Perhaps some clean-up is in order.

   The Wikipedia article on archimedean groups does say that they’re abelian, but perhaps you’re right perhaps in that this ought to be said first. Perhaps some clean-up is in order.

7. • CommentRowNumber7.
   • CommentAuthorGuest
   • CommentTimeJun 18th 2021
   • PermaLink
   Author: Guest
   Format: MarkdownItexTodd wrote: > Replaced the wrong sentence that the real numbers form a terminal archimedean group Is that because, unlike in the case for fields, the trivial group can be trivially made into a linearly ordered group by declaring $0 < 0$ to be false? So the terminal archimedean group would just be the trivial group?

   Todd wrote:

   Replaced the wrong sentence that the real numbers form a terminal archimedean group

   Is that because, unlike in the case for fields, the trivial group can be trivially made into a linearly ordered group by declaring $0 < 0$ to be false? So the terminal archimedean group would just be the trivial group?

8. • CommentRowNumber8.
   • CommentAuthorTodd_Trimble
   • CommentTimeJun 18th 2021
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexYes, of course. Consider also that there are many maps of archimedean groups from $\mathbb{Z}$ to $\mathbb{R}$. In order for $\mathbb{R}$ to be terminal, you'd need exactly one.

   Yes, of course.

   Consider also that there are many maps of archimedean groups from $\mathbb{Z}$ to $\mathbb{R}$. In order for $\mathbb{R}$ to be terminal, you’d need exactly one.

9. • CommentRowNumber9.
   • CommentAuthornLab edit announcer
   • CommentTimeJan 9th 2023
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexmoved material on the Archimedean property in general to its own page [[Archimedean property]] Anonymous <a href="https://ncatlab.org/nlab/revision/diff/archimedean+group/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/archimedean+group/11">v11</a>, <a href="https://ncatlab.org/nlab/show/archimedean+group">current</a>

   moved material on the Archimedean property in general to its own page Archimedean property

   Anonymous

   diff, v11, current