We explain what the algebraic language is, its origins and functions. Also, examples of algebraic expressions and what types they can be.
What is an algebraic language?
The algebraic language is the language of mathematics. That is, to an expression system that uses symbols and numbers to express what we usually communicate through words, and that we allow you to formulate theorems, solve problems, and express formal proportions or relationships of a different nature.
The algebraic language was born, logically, along with algebra, the branch of mathematics that studies the relationship and combination of abstract elements according to certain rules. These elements can be numbers or quantities, but they can also be unknown values or certain numerical ranges, for which letters (known as unknowns or variables) are used.
Originally, this field of knowledge was called al-jabr wa l-muqabala, that is, “the science of the restoration of equilibrium”, as formulated by one of his parents, the Persian astronomer, geographer and mathematician Al-Juarismi (ca. 780-ca. 850). The name came from studying how to move a term from one side of an equation to the other, or how to add one to both sides to preserve the proportion. Over time, al-jabr came to Latin as algeber or algebra.
Seen like this, then, the algebraic language is the language of algebra. The written forms that such language produces are known as algebraic expressions: any number, any equation are perfect examples of it. Using these types of expressions, then, we can “speak” the algebraic language, and communicate relationships and operations that go far beyond the scope of mere arithmetic.
See also: Formal languages
What is an algebraic language for?
As we have said before, the algebraic language is used to construct algebraic expressions, that is, formulations in which numbers, symbols and letters are combined to express a logical and / or formal relationship, in which some amounts are known and others are unknown.
The algebraic expressions, then, are ordered chains of these signs, in which we will find numbers, letters and arithmetic operators. Depending on what they are, we can distinguish between, for example:
- Unknowns (expressing unknown values) or variables (which express non-fixed values), the latter being dependent or independent.
- Arithmetic signs (which express certain arithmetic operations).
- Superscripts or powers (which involve multiplying a number by itself a certain number of times).
- Roots or radicals (which involve dividing a number by itself a certain number of times).
- Features (that express a dependency relationship between two values of two or more expressions).
Examples of algebraic expressions
The following are examples of algebraic expressions:
- 19465 + 1
- 9x + 2
- 6x. 2 (4 + x)
- 2x3
- 8a + 4b = c
- y – 20 (x) = ½
- F (x) = 2 (A, B)
- 4 (a + b)
- 6A + 2B – C = 0
- 4½ = 2
- 2y = x – 2
- 1 / (y + x). 5
- x3 + 2y2 + 9
- [ 53. (a+b) ] – 7
- 9 + 9 + 9 + 9
- 5 + (1 – y) = 3
- 84
- y – x + 1