Empty Set ClassificationDate: 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. Thanks! 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 |
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