Editing Limit ordinal (section)

==Alternative definitions==
Various other ways to define limit ordinals are:
*It is equal to the [[supremum]] of all the ordinals below it, but is not zero.  (Compare with a successor ordinal: the set of ordinals below it has a maximum, so the supremum is this maximum, the previous ordinal.)
*It is not zero and has no maximum element.
*It can be written in the form ωα for α > 0. That is, in the [[Ordinal arithmetic#Cantor normal form|Cantor normal form]] there is no finite number as last term, and the ordinal is nonzero.
*It is a limit point of the class of ordinal numbers, with respect to the [[order topology]]. (The other ordinals are [[isolated point]]s.)

Some contention exists on whether or not 0 should be classified as a limit ordinal, as it does not have an immediate predecessor; 
some textbooks include 0 in the class of limit ordinals<ref>for example, Thomas Jech, ''Set Theory''. Third Millennium edition. Springer.</ref> while others exclude it.<ref>for example, Kenneth Kunen, ''Set Theory. An introduction to independence proofs''. North-Holland.</ref>