The absolute value and relative value comparison method is mainly used to compare the maximum growth, and its most common formula is Ar\( 1+r), where A is the absolute value, usually the final value; R is a relative quantity, that is, the growth rate Ar\( 1+r), that is, the growth amount.
The comparison method of absolute value and relative value is to judge the size of the two growth amounts by analyzing the influence of A and R on the final result.
Divide Ar\( 1+r)=Ar\( 1+r) into two parts: a and r\( 1+r). R\( 1+r) is a increasing function, that is, with the increase of R, the value of r\( 1+r) also increases. So there are:
At the end of the period, a is large, the growth rate R is large, and the increment is large;
When a is almost the same at the end of the period, the greater the growth rate r, the greater the increment;
When the growth rate R is almost the same, the bigger the final A, the bigger the increment.
So, if we know the final value and the growth rate, compare the amount of growth-many times we don't need to calculate, just look at the two parts of A and r/( 1+r), and we can compare the sizes.
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.
Extended data:
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 absolute value of a positive number is itself; The absolute value of a negative number is its reciprocal; The absolute value of 0 is still 0. The absolute value of special zero is both its own and its opposite.
The absolute value of any rational number is non-negative, that is, the absolute value of any rational number is greater than or equal to 0.
The absolute value of any pure imaginary number is the absolute value of the imaginary part (for example:).
When a≥0,; When a<0 point,; Existence.
Comparing the sizes of two negative numbers, the absolute value is larger but smaller. The absolute values of a pair of opposites are equal.
The relative value is the difference between a standard value and the reading of this difference. This standard value is generally an absolute value. Two numbers with the same absolute value but different signs (one positive and one negative, except 0) are relative to each other.
If you record three women as -3 and four men as +4, how many people are there? The calculation method is to add the absolute values of two numbers, that is, seven people. If you ask the difference between men and women, the calculation method is to add the relative numbers, which is+1.
If you take 1 km south as+1 and 2 km north as -2, then ask how many kilometers you have walked. The calculation method is to add the absolute values of two numbers, that is, 3km. If you are asked how many kilometers you have traveled, the calculation method is the sum of relative numbers, which is-1.
If 10 degree to zero degree is marked as+10, and minus 5 degree is marked as -5, how many degrees is the difference between up and down? The calculation method is to add the absolute values of two numbers, that is, 15 degrees. If you ask how many degrees the sum of temperatures is, the calculation method is to add the relative numbers, which is +5.
If the title doesn't say anything positive, for example, the postman delivers letters to the south 10 meters and then to the north 5 meters. Before doing the problem, he must write: remember what is positive, generally don't write again, because it is either positive or negative, only one is known.
So the concept of absolute value is also controversial. Some people don't think the absolute value must be positive. This shows that mathematics is also developing constantly. Moreover, the mathematics we see is only a stage in the historical process, and it has not affected normal learning.
References:
Baidu Encyclopedia-Relative Value
References:
Baidu encyclopedia-absolute value