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Section: 20.14.8 [comparisons], 22.2.1 [container.requirements.general], 220.127.116.11 [thread.thread.id] Status: New Submitter: Matt Austern Opened: 2015-10-08 Last modified: 2015-10-31
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A number of places in the library, including 20.14.8 [comparisons]/14, the Optional container requirements in 22.2.1 [container.requirements.general], and 18.104.22.168 [thread.thread.id]/8, use the phrase "total order". Unfortunately, that phrase is ambiguous. In mathematics, the most common definition is that a relation ≤ is a total order if it's total, transitive, and antisymmetric in the sense that x≤y ∧ y≤x ⇒ x=y. What we really want is a strict total order: a relation < is a strict total order if it's total, transitive, and antisymmetric in the sense that exactly one of x<y, y<x, and x=y holds.
The non-normative note in 25.8 [alg.sorting]/4 correctly uses the phrase "strict total ordering" rather than simply "total ordering".
We could address this issue by replacing "total order" with "strict total order" everywhere it appears, since I think there are no cases where we actually want a non-strict total order, or we could add something in Clause 17 saying that we always mean strict total order whenever we say total order.