About some Bachmann–Landau notations

Question

Let $(u_{n})_{n},(v_{n})_{n}$ two strictly positive real sequences verifying the following property: There exist a positive integer $N$ and there exist a positive real number a such that for all $n>N$ we have $$u_{n}/v_{n}≤a$$ I am asking if there is any obstruction to write $$u_{n}/v_{n}≤a⇔1/a≤v_{n}/u_{n}$$ This question is related to this page: https://en.wikipedia.org/wiki/Big_O_notation#Family_of_Bachmann%E2%80%93Landau_notations

Answer 1

If $x$ and $y$ are positive real numbers, then it holds that

$$ x \le y \iff \frac{1}{y} \le \frac{1}{x}.$$