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!
Method 2 Extension Using Letter Strings:
Single Letters (1-26): Use 'a' to 'z' for numbers 1 to 26.
Two-Letter Combinations (27 onwards): 'aa' = 27 'ab' = 28 'ac' = 29 And so on...
Three-Letter Combinations: After exhausting all two-letter combinations, use 'aaa' for the next numbers.
Conclusion: This creates an unending sequence that can represent all numbers.
Explanation
As described in the chapter, Method 2 uses English letters 'a' to 'z' for numbers 1 to 26. The limitation is that only 26 numbers can be represented. By using strings of multiple letters, similar to how we use multiple digits in the Hindu system, we can extend this to represent all numbers. This is analogous to how positional number systems work.
Solution Steps
Use single letters 'a' to 'z' for numbers 1 to 26.
Extend to two-letter combinations: 'aa' for 27, 'ab' for 28, 'ac' for 29, and so on.
After exhausting two-letter combinations, use three-letter combinations like 'aaa' for the next numbers.
Continue this pattern to create an unending sequence representing all numbers.