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Where's the motivation

  1. Oct 16, 2011 #1
    Where's the motivation for concluding that there are infinitely many unique infinite cardinal numbers?

    I understand the proof for it and accept it, but what other useful implications of this can be drawn in mathematics? It almost seems like Cantor developed this idea in set theory just to say he developed something. It reminds me of the topic of fuzzy logic, sure its a well written idea, and even sort of cool, but where's the usefulness and potential?
     
  2. jcsd
  3. Oct 16, 2011 #2
    I'm not sure abut its functional significance, though my experience with set theory is minimal (at least, a set theorist would think so). But note that the result is motivated largely by the existence of cardinal numbers; once you define them and show they exist, "how many are there?" is a natural question to ask.
     
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