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Date: Mon, 5 Jun 2000 04:56:32 EDT
Subject: Re: [lojban] Transfinite ordinals
To: lojban@egroups.com
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From: pycyn@aol.com
In a message dated 00-06-04 21:20:26 EDT, you write:
<< notice that Lojban has a word for transfinite cardinals, but not for
transfinite ordinals.
Transfinite cardinals (denoted by Hebrew letters with subscripts) tell the
number of elements in a set; transfinite ordinals (denoted by Greek letters)
tell how it is ordered. For instance, the set of all positive integers has
cardinality aleph-null and ordinality omega. The set of all positive integers
and aleph-null still has cardinality aleph-null, but its ordinality is
omega+1.
The set of all ordered pairs of positive integers has ordinality omega*omega,
but its cardinality is still aleph-null.
Anyone want to add a word for these? >>
Will we do better than <.o'obu>? Adding all the paraphenalia of subscripts
and the like, can get most of these. And, of course, there are all those
other order types than the well-ordering (I forget the main ones: eta? and
iota? for dense and continuous?) and even the extreme well-orderings -- of
omegas and then the inaccessibles. If we ever need those (and I hope it is
rarely) we will get the signs we need for them.