Null Sets

Date: 8/23/96 at 20:35:41
From: Anonymous
Subject:  Null Sets

Hello again,

I have a question for which my geometry teacher could not remember the 
answer.  We were talking about sets and he told us that the null set 
is a subset of every set, but he couldn't remember if it was a *
proper* subset of every set.  Thanks.

T.J. Jenkins

Date: 8/25/96 at 7:9:32
From: Doctor Pete
Subject: Null Sets

The null set is not a proper subset of every set. If A is a subset 
of B, the containment is proper if and only if there exists an 
element b in B such that b is not in A. Since every set contains 
itself (i.e. every set is a subset of itself), the null set is a 
subset of the null set. But this containment is not proper; thus the 
null set is not a proper subset of every set.

-Doctor Pete,  The Math Forum
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