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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?
Can anyone help with this please?
Last edited:
... good, what I figured, and the answers to the questions?They are functions that map N to N (natural numbers).
I guess f(n) is just an arbitrary function.
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.
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.
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.
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.
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.