# Union of every language within group of decidable languages is also decidable?

So I was trying to solve following exercise:

Let $$(L_{i})_{i \in \mathbb{N}}$$ be a family of decidable languages – this means that every $$L_{i}$$ is decidable. Then $$\cup_{i \in \mathbb{N}}L_{i}$$ is also decidable. Right or wrong?

The solution states, that this statement is wrong because we can set $$L_{i}:=\{f(i)\}$$ with $$f : \mathbb{N} \rightarrow H_{0}$$ and will therefore receive $$\cup_{i \in \mathbb{N}}L_{i} = H_{0}$$. At the same time $$L_{i}$$ languages are still decidable, for every $$i \in \mathbb{N}$$ because they are finite.

However I still struggle to understand how exactly a language can be decidable with $$f : \mathbb{N} \rightarrow H_{0}$$, because I thought that $$H_{0}$$ was not decidable.