Ordinal Comparison

Let (A,<=) and (B,<=) be well ordered sets with ordinal numbers alpha and beta. Then alpha<beta iff A is order isomorphic to an initial segment of B (Dauben 1990, p. 199). From this, it can easily be shown that the ordinal numbers are totally ordered by the relation. In fact, they are well ordered by the relation.

See also

Well Ordered Set

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Dauben, J. W. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton, NJ: Princeton University Press, 1990.

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Ordinal Comparison

Cite this as:

Weisstein, Eric W. "Ordinal Comparison." From MathWorld--A Wolfram Web Resource.

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