Let denote a finite alphabet, * denote all words over that alphabet, and L denote the function that maps a string to its length, i.e. L : * N (where N denotes the natural numbers) [a] Is L partial, total, or both?

[b] Is L one-to-one? onto? a bijection?

[c] How many words in * have length n?

[d] How many words in * have length n

[e] Explain whether * is finite, countable, or uncountable.

[f] Explain whether P(*) - the set of all subsets over * - is finite, countable, or uncountable. Hint: how is this related to the real numbers in [0, 1).