Algebra uses signs, letters and numbers to enable arithmetic operations.
Algebra is the name that identifies a branch of Mathematics that uses numbers, letters and signs to refer to multiple arithmetic operations. The term has its origins in the Latin algebra , which, in turn, comes from an Arabic word that translates into Spanish as “reduction” or “colation.”
This etymological origin allowed the art focused on the reduction of bones that were dislocated or broken to be known as algebra in times past. This meaning, however, has fallen into disuse.
What is algebra
Today we understand algebra as the mathematical area that focuses on relationships , structures and quantities . The discipline known as elementary algebra , in this framework, is used to carry out arithmetic operations (addition, subtraction, multiplication, division) but, unlike arithmetic, it uses symbols (a, x, y) in instead of using numbers . This allows general laws to be formulated and reference to unknown numbers ( unknowns ), which makes possible 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 have. For example, the 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; Multiplication , for example, is also commutative and associative.
Known as the Fundamental Theorem of Algebra , on the other hand, is a postulate according to which, in a non-constant variable where there are complex coefficients, a polynomial has as many roots as its degree indicates, because the roots are taken into account with their multiplicities. This assumes that the field of complex numbers is closed for algebra operations.
Algebra problems are part of mathematics classes.
Boolean algebra
Control systems , such as connectors and relays, use many components that have two very distinct states: open (conducting) or closed (not conducting). These are called all-or-nothing, or logical , components .
These states are represented with the numbers 1 and 0, which facilitates the systematic study of the behavior of 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 all-or-nothing component can be represented by a logical variable, which means that it can have the value 1 or 0. The group of laws and rules that are taken into account are called Boolean algebra. to operate with this type of variables; Its name comes from the surname of the creator, a self-taught English mathematician whose given name was George and who lived in the 19th century.
Boolean variables in programming
Also known as flags , Boolean variables (a Castilianized term that comes 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 use a resource. Broadly speaking, a Boolean variable is used to record the completion of a certain task; For example, at the beginning of an application the graphics for the interface and music are usually loaded, and a logical variable could be initialized to "false" to wait for said process to complete, and only then change to "true", so so that the program does not try to repeat the steps and can continue forward.