You needn't use "$\mathbb N^{*}$", as $\mathbb N$ already means the integers greater than zero.

The original wording was "ascending function", not "strictly ascending function". A constant function is ascending, but not strictly ascending, so it's not excluded by the original wording.

Hence $f(n) = 4\ \forall n \in \mathbb N^{*}$ satisfies all the originally stated conditions.

Hello,

I do not understand! I think the function \(\displaystyle f(n)=C\) where \(\displaystyle C\) is a constant is neither ascending and neither descending.

Why can not we consider that the function \(\displaystyle f(n)=C\), where \(\displaystyle C\) is a constant, is descending function?

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Really, if we consider \(\displaystyle f(n)=C\) where \(\displaystyle C\) is a constant, then from the imposed condition it follows that \(\displaystyle C=4\), but first to prove that the function \(\displaystyle f(n)=C\), where \(\displaystyle C\) is a constant, is an ascending function and is not an descending function. Thank you very much!

All the best,

Integrator