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Boolean Algebra 𓆩⚪𓆪｜Definition｜1st｜20251119205401-00-⌔
Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and negation (not) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations.
Boolean algebra was introduced by George Boole in his first book The Mathematical Analysis of Logic (1847),1 and set forth more fully in his An Investigation of the Laws of Thought (1854).2 According to Huntington, the term Boolean algebra was first suggested by Henry M. Sheffer in 1913,3 although Charles Sanders Peirce gave the title “A Boolian [sic] Algebra with One Constant” to the first chapter of his “The Simplest Mathematics” in 1880.4 Boolean algebra has been fundamental in the development of digital electronics, and is provided for in all modern programming languages. It is also used in set theory and statistics.5
Printed 2026-06-28.
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Link to original Footnotes
Boole, George (2011-07-28). The Mathematical Analysis of Logic - Being an Essay Towards a Calculus of Deductive Reasoning. ↩
Boole, George (2003) [1854]. An Investigation of the Laws of Thought. Prometheus Books. ISBN 978-1-59102-089-9. ↩
“The name Boolean algebra (or Boolean ‘algebras’) for the calculus originated by Boole, extended by Schröder, and perfected by Whitehead seems to have been first suggested by Sheffer, in 1913.” Edward Vermilye Huntington, “New sets of independent postulates for the algebra of logic, with special reference to Whitehead and Russell’s Principia mathematica”, in Transactions of the American Mathematical Society 35 (1933), 274-304; footnote, page 278. ↩
Peirce, Charles S. (1931). Collected Papers. Vol. 3. Harvard University Press. p. 13. ISBN 978-0-674-13801-8. ↩
Givant, Steven R.; Halmos, Paul Richard (2009). Introduction to Boolean Algebras. Undergraduate Texts in Mathematics, Springer. pp. 21–22. ISBN 978-0-387-40293-2. ↩
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