Some new insights into ideal convergence and subsequences

Some results on the sets of almost convergent, statistically uniformly $I$-convergent subsequences $(s_{n})$ have been obtained by many authors via establishing a one-to-one correspondence between interval $(0,1]$ and collection all given sequence $s=(s_{n})$. However, there are still some gaps in existing literature. In this paper we plan to fill with new results. them easily derived from earlier but they offer deeper insights.