From Boo ean A 9 ebra to Unified Algebra

In t roduct ion This paper is about the symbols and notations of boolean algebra, and about the way the subject is explained. It is about education, and about putting boolean algebra into general use and practice. To make the scope clear, by "boolean algebra" I mean the algebra whose expressions are of type boolean. I mean to include the expressions of propositional calculus and predicate calculus. I shall say "boolean algebra" or "boolean calculus" interchangeably, and call the expressions of this algebra "boolean expressions". Analogously, I say "number algebra" or "number calculus" interchangeably, and call the expressions of that algebra "number expressions". Boolean algebra is the basic algebra for much of computer science. Other applications include digital circuit design, law, reasoning about any subject, and any kind of specifications, as well as providing a foundation for all of mathematics. Boolean algebra is inherently simpler than number algebra. There are only two boolean values and a few boolean operators, and they can be explained by a small table. There are infinitely many number values and number operators, and even the simplest, counting, is inductively defined. So why is number algebra taught in primary school, and boolean algebra in university? Why isn't boolean algebra better known, better accepted, and better used? One reason may be that, although boolean algebra is just as useful as number algebra, it isn't as necessary. Informal methods of reckoning quantity became intolerable several thousand years ago, but we still get along