The Mechanism of Counting
One way of extending the number system in Method 2 is by using strings with more than one letter — for example, we could use 'aa' for 27. How can you extend this system to represent all the numbers? There are many ways of doing it!
With single letters a to z, we can represent numbers 1 through 26.
One natural extension uses two-letter strings in alphabetical order: aa, ab, ac, …, az (26 more numbers = 27 to 52), then ba, bb, …, bz (53 to 78), …, zz (representing 26 + 26² = 702).
But this still ends. To represent ALL numbers, we keep increasing the string length:
Length 1: a, b, c, …, z (26 numbers)
Length 2: aa, ab, …, zz (26² = 676 numbers)
Length 3: aaa, aab, …, zzz (26³ numbers)
and so on indefinitely.
At each string length, there are finitely many strings; but since string length is unbounded, we can represent any positive integer. This is analogous to how the Hindu numeral system uses strings of digits 0–9 of increasing length.
Answer: Use strings of letters of increasing length: length 1 (a–z covers 1–26), length 2 (aa–zz covers 27–702), length 3, and so on — every positive integer is eventually covered.