Algebra Explanations

Algebra is the name that identifies a branch of Mathematics that uses numbers, letters and signs to be able to refer to multiple arithmetic operations. The term has its origin in the Latin algebra, which, in turn, comes from an Arabic word that is translated into Spanish as “reduction” or “collation”.

This etymological origin allowed that in past times, art focused on the reduction of bones that were dislocated or broken was known as algebra. This meaning, however, has fallen out of use.

Today we understand as algebra the mathematical area that focuses on relationships, structures and quantities. The discipline known as elementary algebra, in this framework, serves to carry out arithmetic operations (addition, subtraction, multiplication, division) but which, unlike arithmetic, uses symbols (a, x, y) in instead of using numbers. This makes it possible to formulate general laws and make reference to unknown numbers (unknowns), which enables the development of equations and the analysis corresponding to their resolution.

Elementary algebra postulates different laws that allow us to know the different properties that arithmetic operations possess. For example, addition (a + b) is commutative (a + b = b + a), associative, has an inverse operation (subtraction), and has a neutral element (0).

Some of these properties are shared by different operations; the multiplication, for example, is also commutative and associative.

On the other hand, the Fundamental Theorem of Algebra is known as a postulate according to which, in a non-constant variable where there are complex coefficients, a polynomial has as many roots as its degree marks, because the roots are taken into account with their multiplicities. This assumes that the body of complex numbers is closed for algebra operations.

Boole’s algebra

The systems control, such as connectors and relays, utilize many components which have two very different states: open (conducting) or closed (not conducting). These are called all-or-nothing components, or logical.

These states are represented by the numbers 1 and 0, which facilitates the systematic study of the behavior of the logical components. In turn, a set of common laws and properties are applied that have no direct relationship with the type of element in question (it does not matter if it is a logic gate, a relay or a transistor).

According to all this, any component of type all or nothing can be represented by a logical variable, which means that it can have a value of 1 or 0. Boolean algebra is the group of laws and rules that are taken into account to operate with this type of variables; Its name comes from the name of the creator, a self-taught English mathematician whose first name was George and who lived in the 19th century.

Boolean variables in programming

Also known as flags, Boolean variables (Spanish term and derived from “boolean”, so its pronunciation is “buleanas”) can receive one of two values; These are usually associated with true and false, and in many programming languages ​​it is possible to use the numbers 1 and 0 or the words interchangeably.

Its usefulness is very broad, since in programming everything depends on the skill and creativity of each individual person and it is impossible to determine a single way to structure a code or to use a resource. Broadly speaking, a variable of the Boolean type is used to record the completion of a certain task; for example, at the beginning of an application, the graphics for the interface and the music are usually loaded, and a logical variable could be initialized to “false” to wait for the process to complete, and only then change to “true”, so that the program does not try to repeat the steps and can continue.

Algebra