The **Algebraic language** It is the one that allows to express mathematical relationships. The elements that make up the algebraic language can take the form of numbers, letters or other types of mathematical operators. For instance:* 5 (A + B), XY, 121/7, 10 ^{10}*.

The enormous developments that have been achieved in the field of** mathematical analysis, algebra and geometry** they would have been unthinkable if there were not a common, synthetic language that expresses relationships in a univocal and universal way. Seen in this way, algebraic language facilitates the abstractions of the formal sciences.

### Examples of algebraic expressions

Here are some examples of expressions in algebraic language:

- 5 (A + B)
- XY
- 5
^{2} - 3X-5Y
- (2X)
^{5} - (5X)
^{1/2} - F (X) = Y
^{2} - 9
^{6} - 121/7
- 10
^{10} - (A + B)
^{2} - 100-X = 55
- 6 * C + 4 * D = C
^{2}+ D^{2} - F (X, Y, Z) = (A, B)
- 3 * 8
- eleven
^{2} - F (X) = 5
- (A + B)
^{3}/ (A + B) - LN (5X)
- y = a + bx

### Characteristics of the algebraic language

In the particular cases of the equations, the **‘unknowns’**, which are letters that can be replaced by any number, but adjusted to the requirements of the equation are reduced to one or a few.

In the case of **inequalities,** the change between the relation of ‘equal’ by one of ‘greater’ or ‘less’ causes that instead of obtaining unique results, we find a response range.

Finally, it must be understood that before the establishment of general relationships, some numbers may not be able to comply with them: in a **division A / B** (the quotient of any two numbers), the number 0 is an exception and that cannot be the value of ‘B’.

The algebraic language is nourished by a **variety of tools** in order to simplify the task of mathematical analysis, and it presupposes some facts. Thus, for example, in the absence of a sign between two units, it is assumed that these units are multiplying.

Thus, the ‘by’ sign expressed as ‘X’ or ‘*’ can be omitted, the product operation will still be assumed. On the other hand, some relationships can be expressed in different ways.

The opposite operation of empowerment is **settlement** (such as square root); all expressions of this type can also be written as powers, but with a fractional exponent. So saying ‘the square root of A’ is the same as saying ‘A raised to ½’.

A **additional function** The algebraic language, somewhat more elaborate than the simple relationships between values or unknowns, is the one that arises in the framework of functions: this language is the one that enables the elementary notion of which variables will be the** independent** and what will be the **dependents**, in the case of relationships that can be represented graphically. This is of substantial use in the realm of most of the sciences that involve mathematics.