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Empty Set Classification

Date: 20 Feb 1995 23:30:01 -0500
From: Janet Lowe
Subject: empty sets

Dear Dr. Math,

We would like to know if you would classify an empty set as being 
finite, infinite, or with another classification.

Janet Lowe

Date: 25 Feb 1995 19:48:06 -0500
From: Dr. Ken
Subject: Re: empty sets

Hello there!

According to R. Creighton Buck's _Advanced Calculus_ book, all sets 
are either finite or infinite.  And infinite sets can be classified as either
countable (like the set of positive integers or the set of rational numbers)
or uncountable (like the set of irrational numbers or the set of real
numbers).  Since the empty set is certainly neither countably infinite nor
uncountably infinite, it must be a finite set.  It's almost like asking
whether the number zero is finite or whether it's infinite.  Sure, it's kind
of a bizarre number (for example, it's equal to its own negative), but it's
finite nonetheless.

- Ken "Dr." Math
- Ethan Dr. on Call
Associated Topics:
High School Basic Algebra
High School Sets

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