Explicitly give an infinity of rational numbers who come from below the number $9.123412341234 ...$, Explicitly give an infinity of rational numbers who come from below the number $9.123412341234 ...$, and an infinity who come from above.
I know this number is $\frac{91225}{9999}$, but how can I give that set of numbers?
Also I have to give an infinity of irational numbers who come from below the number $1.989898989898 ...$, and countless who come from above.
Any ideas or hint?

The phrasing “come from below/above” suggests to me that the intent is a monotone sequence converging toward the given number.  How about $\frac{91225n\pm 1}{9999n}$?  For the irrationals, similarly, $\frac{197x \pm 1}{99x}$, where $x$ belongs to any increasing sequence of positive irrationals, such as natural logarithms of integers starting with 2.
