I am always wary of making mistakes when dealing with trigonometric functions and ratios, but I believe that it makes sense to say that $$ |\sin(n)| \leq 1 \implies \frac{1}{2^n}|\sin(n)| \leq \frac{1}{2^n} \implies \Big|\frac{\sin(n)}{2^n}\Big| \leq \Big|\frac{1}{2^n} \Big| $$ Is there anything invalid with this line of reasoning?
2026-03-29 18:37:27.1774809447
Is it correct to assume that if $n \in \mathbf{Z}_+$ then $ \Big|\frac{\sin(n)}{2^n}\Big| \leq \Big|\frac{1}{2^n}\Big|$?
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Nothing is wrong and $n$ can be any real number also.