What Is Boolean Algebra?

Boolean algebra is a division of mathematics that deals with operations on logical values and incorporates binary variables. Boolean algebra traces its origins to an 1854 book by mathematician George Boole, “The Mathematical Analysis of Logic”.

The distinguishing factor of Boolean algebra is that it deals only with the study of binary variables. Boolean variables are most commonly presented with 💛the possible values of 1 (“true”) or 0 (“false”). Variables can also have more complex interpre🧸tations, such as in set theory. Boolean algebra is also known as binary algebra.

Understanding Boolean Algebra

Boolean algebra is different from elementary algebra, as the latter deals with numerical operations and the former deals with logical operations. Elementary algebra is 🐎expressed using basic mathematical functions, such as addition, subtraction, mulꩵtiplication, and division. Boolean algebra deals with conjunction, disjunction, and negation.

The concept of Boolean algebra was first introduced by George Boole in his book “The Mathematical Analysis of Logic,” and further expanded upon in his book “An Investigation of the Laws of Thought.” Since its concept has been detailed, Boolean algebra’s primary use has been in computer programming languages. Its mathematical purposes are used in set theory and statistics.

Boolean Algebra in Finance

Boolean algebra has applications in finance through mathematical modeling of market activities. For example, research into the pricing of 澳洲幸运5开奖号码历史查询:stock options can be aided by the use of a binary tree to represent the range of possible outcomes in the underlying security. In this 澳洲幸运5开奖号码历史查询:binomial options pricing model, w🍸here there are only two possible outc💦omes, the Boolean variable represents an increase or a decrease in the price of the security.

This type of modeling is necessary because, in American options, which can be 澳洲幸运5开奖号码历史查询:exercised anytime, the path of a security’s price is just as important as its final price. The binomial options pricing model requires the path of a security’s price to b🔜e broken into 🌄a series of discrete time ranges.

As such, the binomial options pricing model allows an investor or trader to view the change in the asset price from one period to the next. This a🐼llows them to evaluate the option based on decisions made at different points.

Because a U.S.-based option can be exercised anytime, this allows a trader to determine whether they should exercise an option or hold onto it for a longer period. An analysis of the 澳洲幸运5开奖号码历史查询:binomial tree would allow a trader to see in advance if an option should be exercised. If there is a positive value, then the⛄ option should be exercised. If the value is negative, then the trader should hold onto the position.

The Bottom Line

Boolean algebra deals with operations on logical values and incorporates binary variables. The division of mathematics differs from elementary algebra in that it deals with logical operations, whereas elementary algebra deals with numerical operations.