Let A be the set of words in the Oxford English Dictionary (OED). For each positive integer j, define Aj to be the set of all words with j letters in the OED. For example, the word "discrete" is an element of A8 because the word "discrete" has 8 letters. The longest word in the OED is "" which has 45 letters. You can assume that for any integer i in the range 1 through 45, there is at least one word in the OED that has i letters. Do the sets A1, …, A45 form a partition of the set of words in the OED?