Why they chose maximum and not minimum functions

In summary, the article discusses the use of minimum function in examples to approach the limit as closely as possible. However, in one of the examples, the use of maximum function is seen. The reason for this is not clear as the inequality is not inverted in this case. The article does not provide a clear distinction between when to use maximum and when to use minimum functions.
  • #1
transgalactic
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  • #2
It's not clear what your question is. In the first example you give, they have [itex]|x-a||x-b|< \epsilon[/itex] in order to get |x-a| only, you have to divide both sides by |x-b| "inverting it reverses the inequality. That doesn't happen in the second example- there is no reciprocal.
 
  • #3
when to use MAX when to use MIN ?
 

1. Why is the maximum function used more frequently than the minimum function in scientific research?

The maximum function is used more frequently in scientific research because it allows for the identification of the highest value within a given set of data. This is often useful in determining the upper limit or threshold of a particular phenomenon or process. Additionally, the maximum function is often used in optimization problems to find the most optimal solution.

2. How does the maximum function differ from the minimum function in terms of mathematical operations?

The maximum function differs from the minimum function in that it returns the highest value from a set of data, while the minimum function returns the lowest value. Mathematically, the maximum function is represented by the symbol "max" and the minimum function is represented by the symbol "min".

3. Can the use of the maximum function in scientific research lead to biased results?

The use of the maximum function in scientific research can potentially lead to biased results if the data set is skewed or contains outliers. It is important for scientists to carefully consider the data and the purpose of their research before deciding to use the maximum function.

4. What are some real-life applications of the maximum function in scientific research?

The maximum function is commonly used in a variety of fields such as economics, physics, and biology. For example, in economics, the maximum function can be used to determine the highest price an item can be sold for without exceeding demand. In physics, it can be used to find the maximum velocity of an object. In biology, it can be used to identify the maximum lifespan of a species.

5. Are there any alternative functions to the maximum function that can be used in scientific research?

Yes, there are alternative functions to the maximum function that can be used in scientific research, such as the median and mean functions. These functions can be useful in cases where the data set is skewed or contains outliers, as they provide a more representative value than the maximum function. Scientists should carefully consider the nature of their data before choosing which function to use in their research.

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