hockey777 said:
)The term "Proving Infinum of Set x_n=1" refers to the process of proving that the set of numbers, represented by x_n=1, has an infimum or the smallest possible value.
Proving the infinum of a set is important because it provides a clear understanding of the lower bound or smallest value of the set. This information is useful in various mathematical calculations and proofs.
The infinum of a set is represented by the symbol "inf" followed by the set within brackets, such as inf{x_n=1}.
The most common approach to proving the infinum of a set is by using the definition of infinum, which states that the infinum of a set is the greatest lower bound of the set. This can be proven by showing that the infinum is less than or equal to all elements in the set, and any number greater than the infinum cannot be a lower bound of the set.
No, the infinum of a set x_n=1 is the smallest possible value and cannot be equal to any other number in the set. It is either less than or equal to all elements in the set, but not equal to any of them.