(unsigned comment by anon: 68.43.187.249 00:22, Sep 16, 2004) 

 ==Any set is a subset of itself, but not a proper subset?== 
 I am a novice, but my sense is that Apostol (pg501 of vol II of Calculus 2nd ed) would disagree with this: 
 "Any set is a subset of itself, but not a proper subset" 
 (Unsigned comment by  19:10, Apr 22, 2005) 

 :Both statements follow immediately from the definitions, which are standard. What does Apostol say on pg501?