Little Omega

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.

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CategoryMath