sala: B2-39,  godz. 10⁰⁰ - 12⁰⁰

sala: B2-39,  godz. 10⁰⁰ - 12⁰⁰

Let $\mathbb{N}=A \cup B$ be a partition of the natural numbers. We prove that if $A$ is sufficiently close to being a subsemigroup, then there exists a basic sequence $Q$ where the set of numbers that are $Q$-normal of all orders in $A$ and not $Q$-normal of any orders in $B$ is non empty. Furthermore, these sets will have full Hausdorff dimension under some additional conditions. This stands in sharp contrast to the fact that if a real number is normal of order $k$ for the $b$-ary expansion, then it is also normal of all orders less than $k$.

sala: B2-39,  godz. 10⁰⁰ - 12⁰⁰

sala: B2-39,  godz. 10⁰⁰ - 12⁰⁰