Sequences satisfying strict inequalities and conditions for limsup = liminf

  • Thread starter Thread starter PvtBillPilgrim3
  • Start date Start date
Click For Summary
SUMMARY

This discussion focuses on finding two sequences, (xn) and (yn), that satisfy strict inequalities as outlined in a specific mathematical problem from a PDF document. The user seeks examples of sequences that meet these criteria without needing assistance in proving the inequalities. Additionally, the discussion touches on the conditions under which the limit superior (limsup) equals the limit inferior (liminf), which is a fundamental concept in real analysis.

PREREQUISITES
  • Understanding of sequences and series in mathematics
  • Familiarity with the concepts of limit superior (limsup) and limit inferior (liminf)
  • Knowledge of strict inequalities in mathematical analysis
  • Basic proficiency in real analysis
NEXT STEPS
  • Research examples of sequences that satisfy strict inequalities in real analysis
  • Study the conditions under which limsup equals liminf in sequence convergence
  • Explore the properties of bounded sequences and their implications
  • Examine the role of subsequences in establishing strict inequalities
USEFUL FOR

Mathematics students, educators, and researchers interested in real analysis, particularly those focusing on sequences and inequalities.

PvtBillPilgrim3
Messages
5
Reaction score
0
This isn't a copy of my assignment, but I found the exact same question on the web:

http://www.math.auckland.ac.nz/~waldron/730/1.pdf

It's question 1 on the PDF. I've been trying all night to find inequalties that are strict like it asks for in that particular problem. I don't need help with proving the inequalities, just an example of two sequences (xn) and (yn) that satisfy them to make them strict simultaneously.

I would super appreciate any ideas on this.
I just need help where it says: Find sequences for which all of these inequalities are simultaneously strict. I can't find an example.
 
Last edited by a moderator:
Physics news on Phys.org
Under what conditions does limsup = liminf?
 

Similar threads

Conditions for Strict Inequality in Span Intersection
  • · Replies 2 ·
Replies
2
Views
2K
Help with Math Proof: Bounded Sequence (xn), (yn) & Limsup (xn)
  • · Replies 1 ·
Replies
1
Views
2K
What Are the LimSup and LimInf of the Sequence a_n=(-1)^n(1+1/n)?
  • · Replies 2 ·
Replies
2
Views
3K
MHB What are the best definitions for limsup and liminf in sequences?
  • · Replies 1 ·
Replies
1
Views
3K
Analysis of "X = (xn) Sequence of Strictly Positive Real Numbers
  • · Replies 1 ·
Replies
1
Views
3K
Statistics, Conditional distributions, UMVUE, Rao-Blackwell
  • · Replies 4 ·
Replies
4
Views
2K
MHB Finding limsup & liminf of Sequence of Sets $A_n$
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Do these Bell inequalities rely on probability concept?
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Is this Recursive Pattern in the Collatz Sequence Known?
  • · Replies 3 ·
Replies
3
Views
1K
Sequence of measurable subsets of [0,1] (Lebesgue measure, Measurable)
  • · Replies 11 ·
Replies
11
Views
5K