transgalactic said:
The other supremum sum may be larger due to the inclusion of additional terms or a different method of calculating the sum. This can result in a higher overall value for the sum.
To determine which supremum sum is larger, we must compare the values of each sum. This can be done by simplifying each sum to a common form or by using mathematical techniques such as finding the limit of each sum.
Yes, the other supremum sum can be smaller than the original if the terms are reduced or the method of calculation yields a lower value. This can occur when working with infinite sums or when certain terms are disregarded.
Yes, comparing supremum sums can be used in various fields such as economics, physics, and statistics. It can help determine the maximum possible value of a variable or the highest attainable level of a certain quantity.
Proving that the other supremum sum is larger requires a rigorous mathematical proof. This can be done by using the properties of supremum and infimum, as well as various mathematical techniques such as induction or contradiction.