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What is the biggest ordinal that exists metamathematically?

  1. Mar 9, 2015 #1
    What is the biggest ordinal that exists metamathematically??
  2. jcsd
  3. Mar 9, 2015 #2


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    Whatever the biggest ordinal is, I can name it plus 1. Discuss.
  4. Mar 9, 2015 #3
    Well, if there is not a maximum cardinal metamatemathically existing, ¿which is the colection of this matematical sets than exist metamathematically
  5. Mar 10, 2015 #4
  6. Mar 11, 2015 #5


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    LoL... Damn, I wish I had a slightly better comprehensive math background... :oldbiggrin:
  7. Mar 11, 2015 #6
    But the Graham´s number is mathematically finite, isn´t it? I talk about ordinal numbers transfinite
  8. Mar 11, 2015 #7


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    Given any set - infinite or not - there is another set that is larger. If the set is infinite, then the other set is a "larger infinity" which means that it is so big that there is no way to ever match it up with the first.

    It follows that there is no largest set and the idea of a set of everything makes no sense.
  9. Mar 11, 2015 #8
    Not a set, but it exists the concept of propper class. A class that can´t be in another class
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