Definition:Conditional/Notational Variants/Sign of Illation

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The sign of illation $-\!\!\!<$ is a notation invented by Charles Sanders Peirce to denote the conditional operator.

Peirce derives $-\!\!\!<$ as a variant of the sign $\le$ for less than or equal to, so as to denote that:

$A \mathop {-\!\!\!<} B$

represents the situation such that whenever a particular statement $A$ is true, then so is statement $B$.

It is rarely (if ever) seen nowadays except as a historical curiosity.

Linguistic Note

The word illation derives from the Latin illātiō, whose meaning is logical inference, deduction or conclusion.

Technical Note

The $\LaTeX$ code for \(A \mathop {-\!\!\!<} B\) is A \mathop {-\!\!\!<} B .