From: Martin DeMello <martindemello@...>
Date: 2004-09-21T17:49:37+09:00
Subject: Re: Array#index block and rdetect

"trans.  (T. Onoma)" <transami@runbox.com> wrote:
> 
>   Main Entry: enu�mer�a�ble
>   Pronunciation: i-'n(y)�m-r&-b&l, -'n(y)�-m&-
>   Function: adjective
>   : DENUMERABLE
> 
>   Main Entry: de�nu�mer�a�ble
>   Pronunciation: di-'n(y)�-m&-r&-b&l
>   Function: adjective
>   : capable of being put into one-to-one correspondence
>     with the positive integers
> 
> So "index" must mean this corresponding integer. I would argue that sets and 
> hashes are not technically enumerable, because they're elements can not be 
> accessed as a _function_ of the index, i.e. one-to-one correspondence.

Just for what it's worth, this is a mathematical notion the closest
everyday word for which is "countable". 'Capable of being put into
one-to-one correspondence with the positive integers' merely means you
can count the elements of the set one by one, not that there is any
preferred ordering of the elements. (Although establishing such a
preferred ordering is often the method used to prove that a set is
denumerable, e.g. the rationals.)

martin