# Proof: Inequality |a-c| <= |b-d|

• nhrock3
In summary, "Proof: Inequality |a-c| <= |b-d|" is a significant concept in mathematics, physics, and engineering. It is used to compare and contrast different values or quantities and to determine their relationship. In practical applications, it is used to make predictions and determine the validity of assumptions. The mathematical basis for this inequality is the triangle inequality, and it can be applied to determine the maximum error in measurements or the stability of systems. One real-life example of its use is in economics to compare incomes and determine economic inequality. There are exceptions to this inequality, such as when the values of a and c are equal or when the values of b and d are equal.
nhrock3
prof that if a=<b and c=<d is given than |a-c|=<|b-d|
from the sum of the given we get a+c=<b+d
that as far as i went

hi nhrock3!

(have a ≤ )
nhrock3 said:
prof that if a=<b and c=<d is given than |a-c|=<|b-d|

that's obviously not true …

9 ≤ 10 and 1 ≤ 3

but 9 - 1 > 10 - 3

## 1. What is the significance of "Proof: Inequality |a-c| <= |b-d|" in the field of science?

This inequality is significant in various fields of science, such as mathematics, physics, and engineering. It is used to compare and contrast different values or quantities, and to determine the relationship between them.

## 2. How is this inequality used in practical applications?

This inequality is used in practical applications to make predictions or determine the validity of certain assumptions. For example, in physics, it can be used to calculate the maximum error in a measurement or to determine the stability of a system.

## 3. What is the mathematical basis for this inequality?

The mathematical basis for this inequality is the triangle inequality, which states that the sum of the lengths of any two sides of a triangle is greater than or equal to the length of the third side. This can be applied to the absolute value of differences between two quantities, as seen in the inequality |a-c| <= |b-d|.

## 4. Can you provide an example of how this inequality is used in a real-life situation?

One example of this inequality being used in a real-life situation is in the field of economics. It can be used to compare the incomes of different individuals or countries, and to determine the level of economic inequality.

## 5. Are there any exceptions to this inequality?

Yes, there are exceptions to this inequality. One exception is when the values of a and c are equal, in which case the inequality becomes |0| <= |b-d|, which is always true. Another exception is when the values of b and d are equal, in which case the inequality becomes |a-c| <= |0|, which is also always true.

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