Self-Distributive Structure/Examples
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Examples of Self-Distributive Structures
Arithmetic Mean
Let $\Q$ denote the set of rational numbers.
Let $\circ$ be the operation defined on $\Q$ as:
- $\forall x, y \in \Q: x \circ y := \dfrac {x + y} 2$
That is, $x \circ y$ is the arithmetic mean of $x$ and $y$ in $\Q$.
Then the algebraic structure $\struct {\Q, \circ}$ so formed is a self-distributive quasigroup.