We explain what a variable is and what types exist. Also, what are the uses of variables in various areas.
What is a variable?
A variable or unknown, in mathematics, is a symbol that represents a changing value within a formula, equation or logical approach. This means that its corresponding figure can change, unlike a constant, whose value is fixed.
The variables They are conventionally represented with letters, especially X and Y.. In this way, an indefinite value is expressed, normally to be calculated or determined by solving a problem or a series of mathematical operations. This procedure is known as “clearing” a variable.
So, for example, in a mathematical expression such as X + 1 = 3, the value of X is ignored and must be deduced through study of the formula. In this case, by solving the variable, we obtain that X = 3 -1, that is, X = 2. If the terms of the mathematical expression change, so will the value of the elements present in the equation.
Who invented variables?
Variables began to be used in mathematics in ancient times, when algebra was a relatively new discipline. Its invention is attributed to Diophantus of Alexandria (c. 200-c. 284 AD), in his work Arithmetics (c. 250 AD). One of its greatest scholars was the Persian mathematician and astronomer Al-Juarismi (c. 780-c. 850), author of Compendium of calculation by reintegration and comparison (c. 830).
See also: Algebraic language
Key points
- A variable is a symbol that represents a changing value within a formula, equation or logical approach.
- Variables are used to introduce an indeterminate element, whose value is not known, into a calculation or formula.
- To classify variables, we usually look at the variation in their value, their dependence on other variables or the way of expressing their value.
Variable types
Given that variables are used in different disciplines and contexts, there are several ways to classify them, depending on the criterion used: the variation of their value, their dependence or the way of expressing their value.
Types of variables according to the variation of their value
In mathematics, logic and computer science, there is a distinction between two types of variables, depending on how fixed their value is:
- Free or real variables. They are those variables within a mathematical expression that act as a wildcard, that is, they identify a place where it is possible to enter an arbitrary value and thus have a different result. Therefore, they do not have their own value, but can be replaced by any number.
- Linked or apparent variables. They are those variables whose value has been linked to a range or set of specific values, so that it can continue to vary, but no longer absolutely freely.
Types of variables according to their dependency
In mathematical models and experimental sciences, two types of variables are usually distinguished, depending on whether or not they are linked to another specific variable:
- Independent variables. They are those variables that can be freely manipulated by the researcher, since the variation in their value is not subject to any type of conditions.
- Dependent variables. They are those variables whose value variation is subject to one or other independent variables, so that if the value of those changes, so does that of these.
Types of variables according to their expression
Depending on the way in which they express their value, two types of variables can be distinguished:
- Quantitative variables. They are those variables that are expressed through numerical arguments, that is, whose value can be expressed through numbers.
- Qualitative variables. They are those variables whose value cannot be expressed in numbers, since they refer to characteristics or qualities of a referent.
What are variables used for?
The variables They allow the mathematician or researcher to introduce into their reasoning an element whose value is not fixed.meaning it cannot be predicted. In this way, the formulas and calculations can be adjusted to use the information that is available, and thus obtain logical and verifiable conclusions.
For example, in statistics, variables are used to express an aspect of reality that is unknown, but that is intended to be calculated through empirical methods, such as surveys or surveys. While in computing, they allow the programmer to anticipate the values that a future user could enter into the system and thus plan the responses they will obtain in return.
In conclusion, the variables They serve to express what is unknown for certain.but that can still be calculated or used within scientific reasoning.
References
- Ferrer Llopis, J. (2015). Mathematical analysis of a variable. Ibero-American Cultural and Scientific Association.
- Rodríguez, C., Breña Oré, JL and Esenarro Vargas, D. (2021). Variables in the methodology of scientific research. 3 Sciences.
