Re: Distinct linear orderings on Z

From: Giuseppe Bilotta (bilotta78_at_hotpop.com)
Date: 03/23/05 

Date: Wed, 23 Mar 2005 18:35:57 +0100

Albert Wagner wrote:
> Look at your 'definition' restated, but without changing the
> meaning: A set S is said to be infinite if a proper subset of S
> is also infinite (in which case a bijection would exist).'

Wrong. The original definition makes no statement whatsoever
about the finiteness or not of the subset.

*You* are deducing that the subset is itself infinite
(something which, BTW, you can only deduce if you accept that a
set which is in bijective correspondance with another set has
the same finiteness property; where do you get this from?), and
putting it back in the definition. 

-- 
Giuseppe "Oblomov" Bilotta
Can't you see
It all makes perfect sense
Expressed in dollar and cents
Pounds shillings and pence
                  (Roger Waters)

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