---
tag: M3GFCVX549
kind: concept
name: Huntington's axioms
msc: ["06E05", "03G05"]
sources:
  - url: https://en.wikipedia.org/wiki/Boolean_algebra_(structure)
---

## Summary

Huntington's axioms are a short system of axioms for [[Boolean algebras|0XADJKM699]] in terms of one binary operation $+$ and one unary operation $n$.
Besides commutativity and associativity of $+$, they need only Huntington's equation $n(n(x) + y) + n(n(x) + n(y)) = x$.
Edward Huntington gave this system in 1933, after an earlier set of postulates from 1904.
The question whether Huntington's equation can be replaced by a similar equation of Herbert Robbins became the [[Robbins conjecture|X74S395RZD]].

## Explanations

### L1 human

Read $+$ as "or" and $n$ as "not".
Then Huntington's equation says: "($x$ and not $y$) or ($x$ and $y$)" is the same as $x$, written with "or" and "not" only.
It is surprising that this single law, together with the rules for reordering and regrouping "or", already gives all of Boolean algebra.