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  "body": "\n## Summary\n\nA left-orderable group is a [[group|G5S1M9]] with a total order that is preserved by multiplication on the left.\nEvery [[orderable group|9BM25E20JQ]] is left-orderable, but the converse fails.\n[[Braid groups|BNR4H5GCTP]] are left-orderable, a result of Dehornoy.\nLeft orders link group theory with dynamics, because countable left-orderable groups are the countable groups that act faithfully on the real line by order-preserving homeomorphisms.\n\n## Explanations\n\n### L1 human\n\nImagine lining up the elements of a group so that multiplying everything on the left by a fixed element keeps the line in order.\nMultiplying on the right may scramble it.\nThis is weaker than asking both sides to respect the order.\nFor countable groups, this is the same as acting on the real line by moving points around while keeping their order.\n",
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