Null SetsDate: 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 Check out our web site! http://mathforum.org/dr.math/ |
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