As the title suggests, the question is :
What is the cardinality of all binary sequnces (infinte and finite) that the sequnce 01 does not apper in them ?
I'll tell you where im stuck, let's say f is a function that recieves a natural number and creates a sequence of just ones, i.e : f(6) = (1,1,1,1,1,1), f(2) =(1.1). Uniting this countable sets togheter will generate a countable set, so lets call the orinignal set(the one we need to find his cardinality) A, so A>= 0א because this set is a subset of A.
Also, A is a subset of all binary sqeunces (infinte and finite) and all the binary sqeunces cardinaliy is א, so A <= א.
So right now i have א0 <= A <= א, which does not help me a lot because i need to find out if its א or א0.
Thanks in advance !