I need help with proof with this Please show detailed proof

I need help with proof with this. Please show detailed proof please.

18. Let Alz denote the set of all polynomials with variable z where each coefficient is an element of the nonempty set A. In other words, n-1 +rir roln E N, ri E AV0S is n) n-12 If A is countable, will Al be countable as well? Either prove the state- ment or provide a counter example. (Think about what your answer implies about QLal.)

Solution

1.degree of A[x] is infinite

2.we can get uncountable combinations from A for the co efficients of given polynomial as it has infinite degree

hence A[x] is uncountable