Adición y Sustracción de Números Reales

Study Notes

Real Numbers Addition and Subtraction

Adding real numbers is defined as follows:

For any two real numbers, say a and b, the sum of a and b is denoted by the expression a + b. The sum can be obtained as the number c such that when we a is taken away from b, we get back c. In other words, if we have b - c = a, we call c the sum of a and b. This definition leads naturally to the following properties of addition of reals:

(i) The sum of two real numbers does not depend on their order: a + b = b + a.

(ii) Addition of two real numbers is commutative: a + b = b + a.

(iii) Addition of two real numbers distributes over multiplication: (a + b) * c = a * c + b * c.

Similarly, subtracting one real number from another is done using the difference operation:

If a and b are real numbers, then the difference between a and b is denoted by a - b and it is defined as the number c such that when a is taken away from b, we get back c. In other words, a - b = b - (-a).

Subtraction of real numbers also has properties similar to addition:

(i) The difference between two real numbers is a real number.

(ii) Addition and subtraction of real numbers are inverse operations.

(iii) Subtraction of two real numbers is commutative: a - b = b - a.

(iv) Subtraction of two real numbers distributes over multiplication: (a - b) * c = a * c - b * c.

These properties of real numbers help in understanding and performing operations like addition and subtraction of real numbers.

Description

Aprende sobre la adición y sustracción de números reales, sus propiedades y operaciones relacionadas. Comprende cómo sumar y restar números reales de acuerdo a definiciones específicas y propiedades que rigen estas operaciones matemáticas.