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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.

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.

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.

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).

<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>

 

<p>(Peirce, CP 3.67).</p>

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