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

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Discussion Overview

The discussion revolves around the relationship between two functions, f(n) and g(n), both mapping natural numbers to natural numbers. Participants explore whether the lack of an upper bound on f(n) by g(n) implies a lower bound, and the conditions under which f(n) can be bounded or unbounded.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether g(n) being not an upper bound on f(n) implies it must be a lower bound, suggesting that the relationship is not straightforward.
  • Another participant notes that the nature of g(n) depends on how it is derived and whether f(n) needs to be bounded at all.
  • It is proposed that both f(n) and g(n) are arbitrary functions mapping natural numbers, raising questions about the necessity of bounds.
  • A participant expresses confusion about how to demonstrate the truth of the initial statement regarding bounds, indicating a lack of clarity in the reasoning process.
  • There is a call for clarification on post #4, which reiterates questions about the boundedness of f(n) and the implications for g(n).

Areas of Agreement / Disagreement

Participants express uncertainty regarding the implications of the relationship between f(n) and g(n). There is no consensus on whether g(n) can be considered a lower bound if it is not an upper bound, and the discussion remains unresolved.

Contextual Notes

Participants have not established clear definitions or assumptions regarding the nature of f(n) and g(n), leading to ambiguity in their discussion about bounds.

sneaky666
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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?
 
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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.
 

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