Manipulating inequalities

So, there are no errors. In summary, the conversation discusses the need to find a value for n that satisfies the inequality 1/(n-2) < epsilon. The speaker mentions that 1/epsilon is not always less than epsilon and wonders if there are any errors in their approach. However, it is concluded that there are no errors and the conversation ends with a clarification about the values of epsilon and n.
  • #1
mjjoga
14
0
so I have 1/(n-2). I have that n>max(epsilon+2,1). I need to get 1/(n-2) < epsilon. I know that 1/(n-2)<1/(epsilon+2-2)=1/epsilon. but 1/epsilon is not always less than epsilon. can you see any errors?
 
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  • #2
Your question is unclear.
 
  • #3
mjjoga said:
so I have 1/(n-2). I have that n>max(epsilon+2,1). I need to get 1/(n-2) < epsilon. I know that 1/(n-2)<1/(epsilon+2-2)=1/epsilon. but 1/epsilon is not always less than epsilon. can you see any errors?
Epsilon is typically a small positive number that is much closer to 0 than it is to 1. Unless epsilon is negative, epsilon + 2 will be larger than 1.

1/(n - 2) < epsilon <==> n - 2 > 1/epsilon, making the reasonable assumptions that n > 2 and epsilon > 0.

If epsilon is small and positive, 1/epsilon is generally larger than epsilon.
 

1. What is the purpose of manipulating inequalities in scientific research?

Inequalities can be manipulated in scientific research to better understand relationships between variables and to test hypotheses. By manipulating inequalities, scientists can determine the direction and strength of a relationship between two or more variables, and make predictions about how changing one variable may impact another.

2. What are the different ways to manipulate inequalities in scientific research?

Inequalities can be manipulated using mathematical operations such as addition, subtraction, multiplication, and division. They can also be manipulated by changing the values of variables or by introducing new variables into the equation. Additionally, inequalities can be manipulated through experiments or simulations.

3. How do scientists ensure that their manipulation of inequalities is valid and reliable?

Scientists use statistical methods and controls to ensure the validity and reliability of their manipulations of inequalities. This includes using appropriate sample sizes, controlling for confounding variables, and conducting multiple trials to reduce the impact of chance or random variation.

4. What are some common challenges scientists face when manipulating inequalities in research?

Some common challenges include identifying the appropriate variables to manipulate, selecting the most appropriate statistical methods, and interpreting the results correctly. Scientists also need to consider ethical considerations when manipulating inequalities, such as ensuring that all participants are treated fairly and respecting their rights and privacy.

5. How can the manipulation of inequalities contribute to scientific knowledge?

By manipulating inequalities, scientists can gain a deeper understanding of the relationships between variables and make predictions about how these relationships may change under different conditions. This can lead to the development of new theories and the advancement of scientific knowledge in a particular field.

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