Hyperwebster

The staff at the publishing company realizes that it can partition the words into 26 volumes, one for each letter of the alphabet. So the Hyperwebster now looks like the following: […] The content of the hyperwebster^([sic]) is equivalent to points on a real line (replace A-Z above with 0-9 and observe that it generates all real numbers).

Take Ian Stuart’s Hyperwebster Dictionary. This paradox shows how subtracting infinity from infinity equals… infinity! […] The Hyperwebster is a dictionary of all possible letters and combinations of letters using the 26 letters of the English alphabet. It starts out like this:

According to Stewart, by removing the first letter in every word, we can produce another copy of the Hyperwebster from each of its volumes; that is, 26 identical copies will be generated.

The Hyperwebster and each of its volumes are countably infinite.