Hobbies And Interests
Single Variable Theorems
Single-variable theorems use only the alphabetic letter x, which can represent either 1 or 0, and is used when the exact value is not known. Basic single-variable theorems include x multiplied by 0 equals 0 and x multiplied by 1 equals x. These theorems are the same as in normal mathematics. Other theorems get more specific. however. For example, x multiplied by x, will always equal either 0 or 1, because x can only equal 0 or 1 itself. Furthermore, x plus 1 or x plus x, even when both x's equal 1, equals 1. This defies regular mathematics and is a point of departure for the unique logic of Boolean algebra.
Multivariable Theorems
Multivariable theorems use several alphabetic letters like x, y and z to represent 0 and 1, so there are more possible combinations of these binary problems. Simple multivariable theorems are the same as basic mathematical rules such as the theorem that the variables can be multiplied in any order to produce the same number: xyz=yzx=zyx and so on. In more advanced theorems, however, you enter the special logic of boolean algebra, because each variable can only equal 0 or 1. For example, x plus xy equals x. More complex multivariables utilize more variables such as Theorem 13b, which states (w+x) (y+z) = wy+wz+xy+xz.
Boolean Algebra
As opposed to the regular algebra of numbers, Boolean algebra is the algebra of binary values, 0 and 1, which represent true and false or yes and no. Boolean algebra is often defined as a logic system as opposed to a mathematical system, because it uses deductive reasoning to prove whether a statement or formula is true or not. The Boolean algebra system uses the terms "and," "or" and "not" to mean multiply, add and divide, although the rules are not the same as in standard mathematics because the product or sum of all equations can only equal 1 or 0.
Using Boolean Theorems
Boolean theorems and Boolean algebra were invented in the 19th century as a logical system and later were applied to the logic of switchboards. Nowadays, Boolean algebra and Boolean theorems are used in search engine functions, where search terms are related by and, or and not values. Boolean algebra has also lead to the development of propositional calculus, which analyzes the logical structure of natural language.