There is a finite number of arrangements of letters; thus there is a finite number of definitions.
Is that true if we're allowed to use each letter an increasing number of times? If our stock of letter tokens increases without limit, then can't the number (and length) of our definitions also increase without limit? Certainly the names of the numbers will tend to get longer as the numbers they name increase, and those names will reuse letters to an ever-increasing degree.
Why do you say that the
Why do you say that the number of words is infinite? The OED has only about 600,000, and the number of languages around the world is finite.
There is a finite number of
There is a finite number of arrangements of letters; thus there is a finite number of definitions.
Is that true if we're allowed to use each letter an increasing number of times? If our stock of letter tokens increases without limit, then can't the number (and length) of our definitions also increase without limit? Certainly the names of the numbers will tend to get longer as the numbers they name increase, and those names will reuse letters to an ever-increasing degree.