Yes. (Happy)suvadip said:Find the greatest lower bound, least upper bound, greatest limit point, least limit point of the following
{3/2,5/2,5/3,7/3,7/4,9/4,9/5,11/5,11/6,...}
I have found the respective answers as 3/2, 5/2, 2,2 . Am I right?
The limit superior and limit inferior are mathematical concepts used to describe the behavior of a sequence of numbers. The limit superior, also known as the upper limit or the supremum, is the largest value that the sequence can approach as n approaches infinity. The limit inferior, also known as the lower limit or the infimum, is the smallest value that the sequence can approach as n approaches infinity.
Limit superior and limit inferior are related to sequences because they describe the behavior of a sequence as n approaches infinity. Both concepts help determine the ultimate behavior of a sequence and provide information about the sequence's convergence or divergence.
Limit superior and limit inferior are used in various real-world applications, such as in economics, physics, and engineering. In economics, they are used to analyze stock market trends and predict future values. In physics, they are used to describe the behavior of physical systems. In engineering, they are used to analyze the stability and performance of systems.
The limit superior and limit inferior are related to each other in that the limit superior is always greater than or equal to the limit inferior. This means that the limit superior provides an upper bound for the sequence, while the limit inferior provides a lower bound.
Limit superior and limit inferior can be calculated by finding the supremum and infimum of a sequence, respectively. The supremum is the smallest number that is greater than or equal to all the terms in the sequence, while the infimum is the largest number that is less than or equal to all the terms in the sequence. By finding these values, the limit superior and limit inferior can be determined.