Teaching Haryana (HPSC) Assistant Professor Mock Test 2025 Mathematical Science Analysis Countable and Uncountable Sets
Let X, Y be defined by
\( X=\{\left(x_n\right)_{n \geq 1}:\displaystyle \limsup _{n \rightarrow \infty} x_n=1\), where xn ∈ {0, 1}}
and
\(\displaystyle Y=\{\left(x_n\right)_{n \geq 1}: \lim _{n \rightarrow \infty} x_n\), does not exist, where xn ∈ {0, 1}}.
Which of the following is true?
1
X, Y are countable.
2
X is countable and Y is uncountable.
3
X is uncountable and Y is countable. X
4
X, Y are uncountable.
5
Question Not Attempted