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| Math Central | Quandaries & Queries |
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Question from Justin, a student: Hello there, I was just wondering since the number of primes is infinite, are they equal to infinity or Aleph-null? Thanks a lot for your help with this question, I greatly appreciate it! Sincerely, Justin |
Justin,
Any infinite subset of the natural numbers has the same cardinality as the natural numbers. Listing the elements of the subset in a sequence where each element appears exactly once describes the required 1-1 correspondence. For the primes the sequence is 2, 3, 5, 7, 11, 13, ...
Hope this makes sense.
Victoria
Justin, you know enough to work this out for yourself.
Can you place the prime numbers into a 1-1 correspondence with the natural numbers ("count" them?)
Good Hunting!
RD
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