Can You Help Me Answer Post #4 in Line 2?

  • Context: Undergrad 
  • Thread starter Thread starter sneaky666
  • Start date Start date
  • Tags Tags
    Functions
Click For Summary
SUMMARY

The discussion centers on the relationship between two functions, f(n) and g(n), both mapping natural numbers (N to N). It is established that if g(n) is not an upper bound on f(n), it does not imply that g(n) is a lower bound on f(n). The participants emphasize that f(n) is arbitrary and can be unbounded, raising questions about the nature of g(n) as a bound. The conversation highlights the need for clarity in defining the relationship between these functions to address unanswered queries effectively.

PREREQUISITES
  • Understanding of mathematical functions, particularly those mapping natural numbers (N to N).
  • Familiarity with concepts of upper and lower bounds in mathematical analysis.
  • Basic knowledge of asymptotic notation and its applications in algorithm analysis.
  • Ability to engage in logical reasoning and proof techniques in mathematics.
NEXT STEPS
  • Research the definitions and properties of upper and lower bounds in mathematical functions.
  • Study asymptotic notation, including Big O, Big Omega, and Big Theta.
  • Explore examples of arbitrary functions and their bounds in mathematical literature.
  • Investigate common proof techniques used to establish relationships between functions.
USEFUL FOR

Mathematicians, computer scientists, and students studying algorithm analysis or mathematical functions, particularly those interested in understanding function bounds and their implications.

sneaky666
Messages
64
Reaction score
0
Lets say if g(n) is not an upper bound on f(n), then does that mean g(n) is a lower bound on f(n)?
Can anyone help with this please?
 
Last edited:
Physics news on Phys.org
depends: how did you find g(n)? does f(n) have to be bounded at all?
 
They are functions that map N to N (natural numbers).
I guess f(n) is just an arbitrary function.
 
They are functions that map N to N (natural numbers).
I guess f(n) is just an arbitrary function.
... good, what I figured, and the answers to the questions?

Since f(n) is an arbitrary mapping N to N, does it have to be bounded? Can it not be unbounded in both directions? What does this say about g(n) as a bound?

You did not say that g(n) is arbitrary - so how is it found? Is it selected from all possible N to N mappings to have some special relationship with f(n)?
 
f(n) and g(n) is arbitrary. Both map from N to N.

I think that the statement in the first post is true but I just don't understand how to show this...
 
Line 2, post #4 remains unanswered. It is a repeat of a question asked in post #2.
(If you did answer it, I missed it.)

If you do not answer questions I cannot help you.
 

Similar threads

Undergrad Supremum proof & relation to Universal quantifier
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Help me understand skewness in QQ-plots please
  • · Replies 1 ·
Replies
1
Views
2K
Interpret Riemann sum to determine integral
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Enumerating a Large Ordinal: Can We Find a Limit to the Continuum?
  • · Replies 27 ·
Replies
27
Views
4K
Undergrad Why Does Yₙ Converge to Zero for q < 1/2 in a Random Walk?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Advantage of having more measurements
  • · Replies 56 ·
2
Replies
56
Views
4K
Graduate Show positivity and boundedness of a non-linear system
  • · Replies 2 ·
Replies
2
Views
991
Undergrad Ways to put n balls in m boxes such that exactly k boxes are empty?
  • · Replies 29 ·
Replies
29
Views
4K
Undergrad Understanding Cantor's Diagonalization Proof: A Brief Explanation
  • · Replies 17 ·
Replies
17
Views
3K
Undergrad The general notion of a recurrence relation
  • · Replies 18 ·
Replies
18
Views
3K