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<title>Issue 2547: Container requirements (and other library text) should say "strict total order", not just "total order"</title>
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<p><em>This page is a snapshot from the LWG issues list, see the <a href="lwg-active.html">Library Active Issues List</a> for more information and the meaning of <a href="lwg-active.html#New">New</a> status.</em></p>
<h3 id="2547"><a href="lwg-active.html#2547">2547</a>. Container requirements (and other library text) should say "strict total order", not just "total order"</h3>
<p><b>Section:</b> 22.10.8 <a href="https://wg21.link/comparisons">[comparisons]</a>, 23.2.2 <a href="https://wg21.link/container.requirements.general">[container.requirements.general]</a>, 32.4.3.2 <a href="https://wg21.link/thread.thread.id">[thread.thread.id]</a> <b>Status:</b> <a href="lwg-active.html#New">New</a>
 <b>Submitter:</b> Matt Austern <b>Opened:</b> 2015-10-08 <b>Last modified:</b> 2015-10-21</p>
<p><b>Priority: </b>3
</p>
<p><b>View other</b> <a href="lwg-index-open.html#comparisons">active issues</a> in [comparisons].</p>
<p><b>View all other</b> <a href="lwg-index.html#comparisons">issues</a> in [comparisons].</p>
<p><b>View all issues with</b> <a href="lwg-status.html#New">New</a> status.</p>
<p><b>Discussion:</b></p>
<p>
A number of places in the library, including 22.10.8 <a href="https://wg21.link/comparisons">[comparisons]</a>/14, the Optional container requirements in 
23.2.2 <a href="https://wg21.link/container.requirements.general">[container.requirements.general]</a>, and 32.4.3.2 <a href="https://wg21.link/thread.thread.id">[thread.thread.id]</a>/8, use the phrase "total order". 
Unfortunately, that phrase is ambiguous. In mathematics, the most common definition is that a relation <code>&le;</code> is 
a total order if it's total, transitive, and antisymmetric in the sense that <code>x&le;y &#x2227; y&le;x &rArr; x=y</code>. 
What we really want is a strict total order: a relation <code>&lt;</code> is a strict total order if it's total, transitive, and 
antisymmetric in the sense that exactly one of <code>x&lt;y</code>, <code>y&lt;x</code>, and <code>x=y</code> holds.
</p>
<p>
The non-normative note in 26.8 <a href="https://wg21.link/alg.sorting">[alg.sorting]</a>/4 correctly uses the phrase "strict total ordering" rather than 
simply "total ordering".
</p>
<p>
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.
</p>


<p id="res-2547"><b>Proposed resolution:</b></p>





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