> Even English has no defined ordering for all characters. What is the ordering of punctuation marks? Do upper case or lower case letters go first? How do you deal with white space characters?
This isn't really true; there are well-defined, standardized answers to all of those:
- For purposes of alphabetizing, punctuation marks are completely ignored, as if they weren't present. "Stop me!" and "Stop, me!" are identical strings.
- Case is also ignored. "AAAAAGH" and "aaaAagh" are identical strings.
- Spaces are not ignored. Sort order is determined by the text before the first space. Shorter sorts before longer. "A bird", "a cat", and "a deer" all sort under "a" and above "ab".
Note that these are rules for English, not rules for arbitrary sequences of binary data. They look the way they do because they model the data as a sequence of English words.
> You can't just say "Stop me!" and "Stop, me!" are identical. You have to define which comes first.
Why? All real-world applications of sorting must handle sorting identical objects. Saying that "Stop me!" and "Stop, me!" are identical doesn't cause any problems that aren't also caused by saying "Stop me!" and "Stop me!" are identical.
But they're not identical, they differ by a comma.
It's a desired feature of sorting algorithms that they should be deterministic, in which case arbitrarily ordered input should produce identical output.
Otherwise, having non-deterministic output just makes everything harder -- harder to make comparisons, more work to write tests, etc.
> But they're not identical, they differ by a comma.
This makes as much sense as saying that "Stop me!" and "Stop me!" aren't identical, because one of them is first and the other is second.
It's true, but it's not relevant to sorting them.
Your "desired feature of sorting algorithms" is most commonly realized as the question of whether the algorithm provides a "stable" sort -- that is, whether two values that compare equal are guaranteed to occur in the same order in the (sorted) output that they did in the (unsorted) input. There are applications where this is considered desirable, and many other applications where it isn't. But there are no applications in which it's not possible for two values to compare equal. For the question of stable sorting to arise in the first place, you have to have already realized that you're going to be sorting things that compare equal.
This isn't really true; there are well-defined, standardized answers to all of those:
- For purposes of alphabetizing, punctuation marks are completely ignored, as if they weren't present. "Stop me!" and "Stop, me!" are identical strings.
- Case is also ignored. "AAAAAGH" and "aaaAagh" are identical strings.
- Spaces are not ignored. Sort order is determined by the text before the first space. Shorter sorts before longer. "A bird", "a cat", and "a deer" all sort under "a" and above "ab".
Note that these are rules for English, not rules for arbitrary sequences of binary data. They look the way they do because they model the data as a sequence of English words.