Our system is the liquid water contained in a bath tub. the drain is open at the bottom while water is being poured into it at an equivalent rate so that the water level within the bathtub is not rising. is this process steady-state?

The process described in the problem is steady-state.

Explanation:

The steady-state can be described by the conservation of mass. In a bathtub it will be the same as In=Out+ Accumulation. Since the water has already reached the adequate level and the drain is open, the accumulation is equal to zero, and therefore it is at steady state. This also means that In = Out which is also described in the problem: "the water is poured into the bathtub at an equivalent rate of the water being drained".

a sequence is a function whose domain is the set of natural numbers.

natural numbers are all the negative and positive integers