Notation for subnet of a sequence

Let $$X$$ be a compact topological Space. Consider a nonconstant sequence $$(x_n)_{n\in \mathbb{N}}$$ in $$X$$ such that $$\{x_n:n\in \mathbb{N}\}$$ is an infinite subset of $$X$$. Note that the said sequence can be treated as a net from $$\mathbb{N}$$. Obviously, this sequence has a convergent subnet (which may not be a subsequence) in $$X$$. Now, I am finding it difficult to symbolise this subnet. I am trying to find a notation for this subnet which does not confuse it with subsequence. Any help will be appreciated.

So $$(x_n)_{n \in \mathbb N}$$ is a sequence. A subnet is like this: $$J$$ is a directed set, and for each $$\alpha \in J$$ we have an $$n(\alpha) \in \mathbb N$$. The subnet is then $$(x_{n(\alpha)})_{\alpha \in J}$$. [Some conditions are required, but they are not shown in the notation.]
This is similar to the subsequence notation $$(x_{n_k})_{k \in \mathbb N}$$. But easier to read without a double subscript.