Danielle S.

asked • 02/19/15

Is a set of complex numbers bigger than or smaller than the set of real numbers

Is a set of complex numbers bigger than or smaller than the set of real numbers?

1 Expert Answer

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Mark M. answered • 02/19/15

Math Tutor--High School/College levels
The set of real numbers is a subset of the set of complex numbers because any real number, a, can be written as a + 0i.  So, the set of complex numbers is "bigger" than the set of reals.  
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Alan G.

I think the answer is no, they are the same size. The idea that if one set contains another plus more then it is larger would be true for finite sets. But I've read that the concepts used for determining which infinite sets are larger or smaller than other infinite sets are different.  If you google 'Georg Cantor' you will get more information on that. According to what I've read, there is a proof that the sets of real and complex numbers are the same size even though the complex contains the reals.  Our intuition is not a good guide when dealing with infinity.  
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05/29/17

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