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The initial sentence has always bothered me > To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots What's so perniciou
by protonfish 8y ago
The initial sentence has always bothered me
> To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots
What's so pernicious about them? I don't see it. It seems like a clear and intuitive way to communicate a sequence to me. I even wrote a little range generator in JS to explore parsing declarations like that. https://github.com/chrisbroski/iterize https://github.com/chrisbroski/iterize It seems to work fine.
- umanwizard 8y agoThat notation is ambiguous. It doesn't cause a problem for humans since we can infer the correct meaning from the context, but it would for computers. For example, does 3, 5, ... 11 mean the odd numbers between 3 and 11 inclusive, or the primes between 3 and 11 inclusive?
- SiempreViernes 8y agoNo, it is ambiguous for humans too as evidenced by the gazillions of problems of the form "N1, N2, N3, what number comes next?". Just decide on some rule for how decide and let people make their own standard if they don't like it.
- kvakil 8y agoOf course the answer is N1 - 3 N2 + 3 N3, since that naturally completes the cubic interpolating polynomial.
- dharmon 8y agoI _think_ he calls them pernicious because of the ambiguity. 2,3,4,12 is also a "subsequence of natural numbers", but probably not what was meant by 2,3,...,12. You might counter that ... means the complete subsequence, but what do you mean by "complete"? If I write 2,4,6,8,...,24, you probably want the ... to mean 10,12,14,...[1], not 9,10,11,12,... Basically by the time you make ... precise, you are better off just writing the mathematical notation. [1] See what I did there? ;)
- deleted 8y ago[deleted]