## FANDOM

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$$\omega$$ (pronounced "omega") is the first transfinite ordinal, the smallest ordinal greater than all the positive integers. In the von Neumann definition of ordinals, it is equal to the set of nonnegative integers $$\mathbb{N}$$.

In the Wainer hierarchy, the fundamental sequence of $$\omega$$ is $$0,1,2,\ldots$$. Using this hierarchy, the following holds: