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0 pointsRayhem4y ago0 comments

> Because starting with 0 is neither math nor array indexing in general.

It very, very much is. Polynomials all start at a zero "index", as does just about every expansion I can think of (Fourier, Bessel, Legendre, Chebyshev, Spherical Harmonic, etc.) Combinatorics, too, make lots of use of zero indices and zero-sized sets. As for arrays, I'll leave it to Dijkstra[1] to explain why zero indexing is most natural. Zero indexing overwhelmingly makes the most sense in both math and computers because indexing is a different operation than counting.

[1]: https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/E...

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6 comments · 2 top-level

coldtea4y ago· 4 in thread

>It very, very much is. Polynomials all start at a zero "index"

Notice how you had to put index in quotes.

Because it's not an index, it's the degree of each polynomial term, which is a power.

RayhemOP4y ago

Notice how you're ad homenim-ing the structure of the argument and not the argument itself? I do not at all see how putting quotes around that word invalidates the argument. I did so because mathematical literature doesn't refer to it as an index (rather as a degree as you mentioned), but it very much does index each monomial. There are an infinite number of index sets for each polynomial -- just as i can index the i'th monomial, so can (i - 7), or (i - 239842), or (i - pi) -- but one of them is obviously the most natural (pun intended).

coldtea4y ago

>I do not at all see how putting quotes around that word invalidates the argument

When the argument is:

  [0] is very, very much is [natural for indexes]

and as an example for that points to something that's not an index -- and the person making the argument knows it is not an index, so they have to put index in quotes:

  Polynomials all start at a zero "index"

...then pointing this out, does invalidate the argument. It might not prove that the opposite is true, but it sure does invalidate the argument.

Notice also how there's no ad-hominen in my response (this or the previous one) as you claim. I argue against the case and the choice of example, not against who wrote it.

FabHK4y ago

GP was addressing the argument. Using the word "you" in the reply does not make it ad hominem.

(For more than you ever wanted to know about this, The Ad Hominem Fallacy Fallacy covers it exhaustively and entertainingly:

https://laurencetennant.com/bonds/adhominem.html )

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edflsafoiewq4y ago

The coefficients are indexed. The n on a_n in Σ a_n X^n is an index.

markkitti4y ago

For some of these polynomials such as Fourier polynomials, it is natural to think about negative subscripts from a pure mathematical perspective. While these can mapped into non-negative integers, it is often intuitive to use the "negative subscripts" as indexes necessitating methods such as `fftshift`. For many of these polynomials the concept of where they "start" is arbitrary.

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