The meaning of absolute value Absolute value is the distance from a point corresponding to a number on the exponential axis to the origin, which is represented by "||". |b-a| or |a-b| represents the distance between the point representing a and the point representing b on the number axis.
In mathematics, the absolute value or the modulus | x | is non-negative, regardless of its sign, that is |x | = x means positive x, | x | = -x means negative x (in this case -x is positive), and | 0 | = 0. For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be considered as the distance from zero.
The generalization of absolute value of real number appears in various mathematical settings, such as complex number, quaternion, ordered ring, field and vector space to define absolute value. Absolute value is closely related to concepts such as size, distance and norm in various mathematical and physical environments.
The simplification method of absolute value formula means that the value must be positive, and the absolute value sign is removed according to the principle of "the same sign is positive and the different sign is negative". The sign of the absolute value is negative. When the absolute value is removed, a negative sign must be added to ensure that the whole value is positive, that is, when: │a│=a(a is positive, that is, when A > = 0).
│ A │ =-A (when A is negative, that is, a≤0) There is nothing special about the simplification method.