Re: Distinct linear orderings on Z

From: Daryl McCullough (stevendaryl3016_at_yahoo.com)
Date: 03/23/05 

Date: 23 Mar 2005 12:09:18 -0800

Albert Wagner says...
>
>Giuseppe Bilotta wrote:

>> Wrong. The original definition makes no statement whatsoever
>> about the finiteness or not of the subset.
>
>Of course it doesn't explicitly. But the implication is obvious.
>Is a pickpocket who works in gloves innocent of theft?

A circular definition is one in which the word to be defined
appears in the definition. The definition for "infinite" is
not circular, since the word "infinite" does not appear in it:

    There exists a bijection between S and a proper subset of S

Are you trying to say that the meaning of "bijection" implicitly
involves the word "infinite"? Are you trying to say that the phrase
"proper subset" implicitly involves the word "infinite"? How is
the definition implicitly circular? 

--
Daryl McCullough
Ithaca, NY

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