X-Message-Number: 26695
Date: Mon, 25 Jul 2005 21:27:54 -0700
From: Mike Perry <>
Subject: Once More on Identity vs Equivalence
References: <>

I respond to Thomas Donaldson's comments:

>You say that 2 sets are identical if
>their members are the same, and thus give a circular definition.

Only informally did I say that (or that's how it should be taken at any 
rate). My actual definition is that X and Y are identical iff, for all z, z 
is a member of X iff z is a member of Y. So I really say nothing directly 
(formally) about the elements of X and Y being "the same".

>Nothing prevents us from considering a set of sets which are
>"identical" in the sense that they differ only on a set of measure
>0, where "measure" is the Lebesgue measure on the real line.
>Well, you might say, such sets do not have the same elements.

Yes, and that's why I'd call them equivalent rather than identical, the 
notion of equivalence *in this case* meaning "symmetric difference (set 
difference) has Lebesgue measure zero". For mathematical "identity" your 
options are narrower.

Mike Perry

Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=26695