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tech / sci.math / Re: Why do mathematicians leave everything out of a set?

Re: Why do mathematicians leave everything out of a set?

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Date: Fri, 7 May 2021 07:51:09 -0700 (PDT)
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Subject: Re: Why do mathematicians leave everything out of a set?
From: Dan_Chri...@sympatico.ca (Dan Christensen)
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by: Dan Christensen - Fri, 7 May 2021 14:51 UTC

On Friday, May 7, 2021 at 12:10:30 AM UTC-4, mitchr...@gmail.com wrote:
> They can't store infinite element anywhere in a set.

0 is an element of the set of natural numbers N. To stretch a metaphor, you might say that 0 is "stored" in N. There are infinitely many elements in N.

To answer your original question, an empty set is a very useful construct. Consider the subset of N consisting of all natural numbers less than 0. Since there are no such natural numbers, we say that such a set is empty. Now, isn't that handy?

Dan

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Subject	Author
Re: Why do mathematicians leave everything out of a set?	Dan Christensen