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Clarify set1#subset #5

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lars-hellstrom opened this issue Jul 20, 2017 · 1 comment
Open

Clarify set1#subset #5

lars-hellstrom opened this issue Jul 20, 2017 · 1 comment
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@lars-hellstrom
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When I was struggling with issue #4, it started to worry me that set1#subset was being rendered as \subset, since I'm used to interpreting that glyph as "proper subset", although I of course am aware of the "just subset" interpretation. The problem is that looking up the subset symbol in the set1 CD does nothing to dispel the ambiguity — if anything it entrenches the ambiguity by only stating transitivity as an FMP of set1#subset, notably the one property that "subset" and "proper subset" have in common!

Reading the whole of set1.xhtml does clarify the issue, since there is a separate symbol set1#prsubset that when contrasted against set1#subset clearly denotes "proper subset" (however, the MathML rendering of both are the same!), but this is not something you easily do when confused about the meaning. Therefore I would suggest adding as a first FMP of set1#prsubset the following:

    <FMP>
      <OMOBJ xmlns="http://www.openmath.org/OpenMath">
        <OMA><OMS cd="logic1" name="equivalent"/>
          <OMA><OMS cd="set1" name="subset"/>
            <OMV name="A"/>
            <OMV name="B"/>
          </OMA>
          <OMBIND>
            <OMS cd="quant1" name="forall"/>
            <OMBVAR>
              <OMV name="x"/>
            </OMBVAR>
            <OMA><OMS cd="logic1" name="implies"/>
              <OMA><OMS cd="set1" name="in"/>
                <OMV name="x"/>
                <OMV name="A"/>
              </OMA>
              <OMA><OMS cd="set1" name="in"/>
                <OMV name="x"/>
                <OMV name="B"/>
              </OMA>
            </OMA>
          </OMBIND>
        </OMA>
      </OMOBJ>
    </FMP>

This is of course a candidate for a DefMP, but that's a later issue.

Also changing the rendering to use \subseteq would be nice, but I'm not sure if there could be political issued involved in that.

@car222222
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Check if any of this has to agree with something in the MathML documentation, especially wrt the symbols used for subset and prsubset.

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