Thread Rating:
  • 1 Vote(s) - 5 Average
  • 1
  • 2
  • 3
  • 4
  • 5
[MO] Is there a tetration for infinite cardinalities? (Question in MO)
#5
I'm not really sure that is that easy...
The problem is that cardinals and ordinals are different and we need a good recursive definition of the tetration over the cardinals.

I mean, is true that but we have also that every transfinite ordinal below is countable and thus has cardinality



and I guess that we always have



For example, all the epsilon ordinals are countable.


Back to the topic. Tommy, when you say inaccessible ordinal you mean "strongly inaccesible" cardinals right? The ones that give us models of ZFC?

I don't even understand how you can take the natural logarithm of a cardinal number...

Note also that cardinal and ordinal exponentiation aren't the same.

MathStackExchange account:MphLee
Reply


Messages In This Thread
RE: [MO] Is there a tetration for infinite cardinalities? (Question in MO) - by MphLee - 12/02/2014, 02:40 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Kneser method question tommy1729 9 1,370 02/11/2020, 01:26 AM
Last Post: sheldonison
  A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 3,753 02/18/2019, 10:34 PM
Last Post: Micah
  Math overflow question on fractional exponential iterations sheldonison 4 4,371 04/01/2018, 03:09 AM
Last Post: JmsNxn
  [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 1,426 03/20/2018, 12:16 AM
Last Post: tommy1729
  Sexp redefined ? Exp^[a]( - 00 ). + question ( TPID 19 ??) tommy1729 0 1,798 09/06/2016, 04:23 PM
Last Post: tommy1729
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 5,630 05/06/2014, 09:47 PM
Last Post: tommy1729
  Another question! JmsNxn 4 4,641 08/27/2013, 06:57 PM
Last Post: JmsNxn
  Very curious question JmsNxn 3 4,102 08/20/2013, 08:56 PM
Last Post: JmsNxn
  Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 7,526 07/17/2013, 09:46 AM
Last Post: Gottfried
  Question about curvature tommy1729 0 1,849 12/15/2012, 11:38 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)