Just as
AlephNought is the "number" used to represent the cardinality of the set containing all the integers from zero onwards,
LittleOmega is the "number" used to represent that set
with its ordering. It is the first ordinal infinity.
Note that unlike
AlephNought, adding one to
LittleOmega does give a different answer from
LittleOmega. Specifically:
- w = 1+w < w+1
- w+n < 2w for all non-negative integers n
- nw < w^2 for all non-negative integers n
For more about this you really need to read about
TransfiniteArithmetic.
CategoryMath