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The "regular non-invertible addition" is signified by "+,", corresponding to what we'd call the inclusive disjunction of logical terms or the union of their extensions as sets.
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The sign <math>^{\backprime\backprime} +\!\!, {}^{\prime\prime}</math> denotes what Peirce calls "the regular non-invertible addition", corresponding to the inclusive disjunction of logical terms or the union of their extensions as sets.
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The "invertible addition" is signified in algebra by "+", corresponding to what we'd call the exclusive disjunction of logical terms or the symmetric difference of their sets, ignoring many details and nuances that are often important, of course.
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The sign <math>^{\backprime\backprime} + ^{\prime\prime}</math> denotes what Peirce calls "the invertible addition", corresponding to the exclusive disjunction of logical terms or the symmetric difference of their extensions as sets.
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But the notation has other recommendations. The conception of ''taking together'' involved in these processes is strongly analogous to that of summation, the sum of 2 and 5, for example, being the number of a collection which consists of a collection of two and a collection of five. (CP 3.67).
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<p>But the notation has other recommendations. The conception of ''taking together'' involved in these processes is strongly analogous to that of summation, the sum of 2 and 5, for example, being the number of a collection which consists of a collection of two and a collection of five.</p>
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<p>(Peirce, CP 3.67).</p>
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