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Omni-MATH / Does the set {1,2,3,...,3000} contain a subset A consisting of 2000 numbers that x∈A implies 2x notin A ?!! :?:

Problem

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problem

Does the set {1,2,3,...,3000}\{1,2,3,...,3000\} contain a subset A A consisting of 2000 numbers that x∈Ax\in A implies $2x \notin A$ ?!! :?:
Plain-text mathematical notation (without MathML)
Does the set {1,2,3,...,3000} contain a subset A consisting of 2000 numbers that x∈A implies $2x \notin A$ ?!!  :?:
Original LaTeX notation
Does the set $\{1,2,3,...,3000\}$ contain a subset $ A$ consisting of 2000 numbers that $x\in A$ implies $2x \notin A$ ?!!  :?:

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