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I've been working with ordinals recently and was wondering how to think about the size of some ordinals relative to others. For example, $\omega < \omega +1$ as ordinals, but they have the same cardinality, so they are the same "size". So, what is really meant by saying $\omega < \omega +1$? Is it appropriate to think of $\omega +1$ as being "bigger" than $\omega$? I am just trying to get some intuition for situations like this. Any help is appreciated.

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closed as unclear what you're asking by Andrés E. Caicedo, Xander Henderson, bof, user91500, Claude Leibovici Sep 24 '17 at 9:16

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