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**Subject**: **Re: 1-based indexing in Lua or the one without zero**
**From**: Dirk Laurie <dirk.laurie@...>
**Date**: Tue, 24 Apr 2018 21:47:10 +0200

2018-04-24 19:26 GMT+02:00 Viacheslav Usov <via.usov@gmail.com>:
>> Talking about notation - I do recall from my days of using mathematics,
>> that the index of a summation was more likely to run from 1 to n.
>
> I am not exactly sure what you mean by "using mathematics", but the use of
> index zero to denote the initial element in a series has been standard since
> at least Cauchy's Cours d'Analyse (1821), where in section 6.1 he wrote u_0,
> u_1, u_2, u_3, etc, to introduce infinite series, and three lines below, s_n
> = u_0 + u_1 + u_2 + .. + u_{n - 1} to define its partial sum.
>
> Way before any C programmers existed.
It is natural in the context of Taylor series and polynomials.
Of course, there are Laurent series too, where you start at a negative index :-)

**References**:
**Re: 1-based indexing in Lua, ***KHMan*
**Re: 1-based indexing in Lua, ***Ahmed Charles*
**Re: 1-based indexing in Lua, ***Oliver Kroth*
**1-based indexing in Lua or the one without zero, ***ag*
**Re: 1-based indexing in Lua or the one without zero, ***Francisco Olarte*
**Re: 1-based indexing in Lua or the one without zero, ***Dirk Laurie*
**Re: 1-based indexing in Lua or the one without zero, ***Francisco Olarte*
**Re: 1-based indexing in Lua or the one without zero, ***Axel Kittenberger*
**Re: 1-based indexing in Lua or the one without zero, ***Oliver Kroth*
**Re: 1-based indexing in Lua or the one without zero, ***Axel Kittenberger*
**Re: 1-based indexing in Lua or the one without zero, ***steve donovan*
**Re: 1-based indexing in Lua or the one without zero, ***Viacheslav Usov*