What is greater than omega?

A fundamental approach to defining ordinals involves treating them as collections, specifically, as sets containing all smaller ordinals. This perspective fosters a deeper understanding of the hierarchical structure inherent within ordinal arithmetic.

When comparing two ordinals, the notion of 'largeness' becomes crucial. We establish that an ordinal is larger than another if the smaller ordinal forms a part of the larger ordinal's set. This criterion serves as the cornerstone for determining ordinal precedence.

As an illustrative example, let's consider the comparison between 'omega' and 'omega plus one.' In this context, 'omega plus one' is deemed 'larger' than 'omega' because 'omega' is inherently included within the set that constitutes 'omega plus one.'

Ordinals can be conceptually understood as a progression beyond the concept of infinity. Imagine an entity that surpasses the boundless quality of infinity by one unit. This imaginative construct highlights the intricate nature of ordinal numbers.

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