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

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In summary, the conversation discusses the relationship between two functions, f(n) and g(n), both of which map from natural numbers to natural numbers. It is suggested that g(n) may be a lower bound on f(n) if g(n) is not an upper bound on f(n). However, it is also questioned whether f(n) must be bounded at all and if it can be unbounded in both directions. It is noted that both f(n) and g(n) are arbitrary functions, and the statement in the initial post is believed to be true but the method of proving it is unclear. A question from an earlier post remains unanswered, and it is mentioned that without responding to questions, further assistance cannot be provided.
  • #1
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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  • #2
depends: how did you find g(n)? does f(n) have to be bounded at all?
 
  • #3
They are functions that map N to N (natural numbers).
I guess f(n) is just an arbitrary function.
 
  • #4
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)?
 
  • #5
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...
 
  • #6
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.
 

1. What are upperbounds of functions?

Upperbounds of functions refer to the maximum possible value that a function can take for a given input. It is the largest number that the function can output and it helps in understanding the behavior and limitations of the function.

2. How are upperbounds of functions calculated?

The computation of upperbounds of functions depends on the type of function. For linear functions, the upperbound can be easily calculated by finding the slope of the line. For more complex functions, mathematical techniques such as calculus and limit evaluation are used to determine the upperbound.

3. Why are upperbounds of functions important?

Upperbounds of functions provide valuable information about the range and behavior of a function. They help in identifying the maximum possible output of a function, which is useful in optimization problems and in understanding the limitations of a system or process.

4. Can upperbounds of functions change?

Yes, upperbounds of functions can change depending on the input and the function itself. For example, if the input of a function is limited to a smaller range, the upperbound may decrease. Additionally, if the function is modified, the upperbound may also change.

5. How do upperbounds of functions relate to real-world applications?

Upperbounds of functions have various real-world applications, such as in engineering, economics, and computer science. In engineering, upperbounds help in determining the maximum load or stress that a structure can withstand. In economics, upperbounds can be used to understand the maximum profit or cost of a business model. In computer science, upperbounds are useful in analyzing the time and space complexity of algorithms.

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