Question

The domain of a sequence can include decimals and irrational numbers.

Answer 1

No, that's not true.  The input variable of a sequence is called the index, which is a counter, such as 1, 2, 3, 4, ...   Note that all of these counters are positive integers.  Normallly I use index i = 1 to denote the first term of a sequence, i = 2 the second term, and so on.

Decimals and irrational numbers are completely unsuitable for serving as such counters.