# Definition:Conditional/Notational Variants/Sign of Illation

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## Definition

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`

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## Sources

- 1885: Charles Sanders Peirce:
*On the Algebra of Logic: A Contribution to the Philosophy of Notation*(*Amer. J. Math.***Vol. 7**: 180 – 202)