Why the the other supremum sum is bigger

  • Thread starter Thread starter transgalactic
  • Start date Start date
  • Tags Tags
    Sum Supremum
Click For Summary
SUMMARY

The discussion revolves around the mathematical property of supremum sums, specifically the inequality sup(xn + yn) ≤ sup{xn} + sup{yn}. Participants clarify that while the supremum of the sum of two sequences cannot exceed the sum of their individual suprema, it can indeed be less than that sum in certain cases. An example provided illustrates this with sequences where xn and yn alternate values, resulting in a supremum of 1 while their individual suprema total 2. This highlights the nuances of supremum calculations in mathematical analysis.

PREREQUISITES
  • Understanding of supremum and infimum concepts in real analysis
  • Familiarity with sequences and their limits
  • Basic knowledge of inequalities in mathematics
  • Ability to interpret mathematical notation and proofs
NEXT STEPS
  • Study the properties of supremum and infimum in real analysis
  • Explore examples of sequences that demonstrate supremum behavior
  • Learn about convergence and divergence of sequences
  • Investigate the implications of supremum in functional analysis
USEFUL FOR

Mathematicians, students of real analysis, and anyone interested in understanding the properties of supremum sums and their applications in mathematical proofs.

transgalactic
Messages
1,386
Reaction score
0
Last edited by a moderator:
Physics news on Phys.org
transgalactic said:
i can't understand this part of the solution..

its seems like the same thing

Hi transgalactic! :smile:

That's sup(xn + yn) ≤ sup{xn} + sup{yn} …

the sum of two things can't be larger than the sum of their maximum possible values …

but it can be smaller (for example, xn = 0 and yn = 1 for n odd, but xn = 1 and yn = 0 for n even … then sup(xn + yn) = 1, but sup{xn} + sup{yn} = 2)

what's worrying you about that? :smile:
 
ahh thanks
:)
 

Similar threads

Can You Solve a Problem Using the Definition of Supremum?
  • · Replies 2 ·
Replies
2
Views
920
N times opeparations(lenear algebra)
  • · Replies 4 ·
Replies
4
Views
1K
Infimum and Supremum, when they Do not exist in finite sets
  • · Replies 8 ·
Replies
8
Views
9K
What is the dimension of the subspace formed by two vectors in R3?
  • · Replies 12 ·
Replies
12
Views
2K
Is the Maximum Always the Same as the Supremum in an Open Interval?
  • · Replies 5 ·
Replies
5
Views
3K
Supremum and Infimum of a Set Containing Rational Numbers
  • · Replies 7 ·
Replies
7
Views
2K
How to prove that something is the supremum of a set?
  • · Replies 5 ·
Replies
5
Views
8K
Undergrad Supremum = least upper bound, anything > supremum?
  • · Replies 8 ·
Replies
8
Views
2K
Dimension of orthogonal subspaces sum
  • · Replies 4 ·
Replies
4
Views
2K
How to know which is bigger? (Comparing two infinite series)
  • · Replies 16 ·
Replies
16
Views
2K